Exact Tape Traces, Canonical Global Rankings and Explicit Recognizer Loops
This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.
This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20261015-advance-20261113-r05-turing-machine-decision-model-foundations · 2026-10-15 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
Field order uses a source-bound presentation supplement; canonical JSONL and mathematical answers are unchanged.
Field-order and source-binding data
1. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q00, q10, qa0, qr0], input_alphabet=[00], tape_alphabet=[00, X0, _0], blank=_0, start=q00, accept=qa0, reject=qr0, transitions=[[q00, 00, q10, X0, R], [q00, _0, qr0, _0, S], [q10, _0, qa0, _0, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q00, q10, qa0, qr0], [00], [00, X0, _0], _0, q00, qa0, qr0, [[q00, _0, qr0, _0, S], [q00, 00, q10, X0, R], [q10, _0, qa0, _0, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q00, q10, qa0, qr0], [00], [00, X0, _0], _0, q00, qa0, qr0, [[q00, _0, qr0, _0, S], [q00, 00, q10, X0, R], [q10, _0, qa0, _0, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
2. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q01, q11, qa1, qr1], input_alphabet=[01], tape_alphabet=[01, X1, _1], blank=_1, start=q01, accept=qa1, reject=qr1, transitions=[[q01, 01, q11, X1, R], [q01, _1, qr1, _1, S], [q11, _1, qa1, _1, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q01, q11, qa1, qr1], [01], [01, X1, _1], _1, q01, qa1, qr1, [[q01, _1, qr1, _1, S], [q01, 01, q11, X1, R], [q11, _1, qa1, _1, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q01, q11, qa1, qr1], [01], [01, X1, _1], _1, q01, qa1, qr1, [[q01, _1, qr1, _1, S], [q01, 01, q11, X1, R], [q11, _1, qa1, _1, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
3. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q02, q12, qa2, qr2], input_alphabet=[02], tape_alphabet=[02, X2, _2], blank=_2, start=q02, accept=qa2, reject=qr2, transitions=[[q02, 02, q12, X2, R], [q02, _2, qr2, _2, S], [q12, _2, qa2, _2, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q02, q12, qa2, qr2], [02], [02, X2, _2], _2, q02, qa2, qr2, [[q02, _2, qr2, _2, S], [q02, 02, q12, X2, R], [q12, _2, qa2, _2, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q02, q12, qa2, qr2], [02], [02, X2, _2], _2, q02, qa2, qr2, [[q02, _2, qr2, _2, S], [q02, 02, q12, X2, R], [q12, _2, qa2, _2, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
4. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q03, q13, qa3, qr3], input_alphabet=[03], tape_alphabet=[03, X3, _3], blank=_3, start=q03, accept=qa3, reject=qr3, transitions=[[q03, 03, q13, X3, R], [q03, _3, qr3, _3, S], [q13, _3, qa3, _3, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q03, q13, qa3, qr3], [03], [03, X3, _3], _3, q03, qa3, qr3, [[q03, _3, qr3, _3, S], [q03, 03, q13, X3, R], [q13, _3, qa3, _3, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q03, q13, qa3, qr3], [03], [03, X3, _3], _3, q03, qa3, qr3, [[q03, _3, qr3, _3, S], [q03, 03, q13, X3, R], [q13, _3, qa3, _3, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
5. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q04, q14, qa4, qr4], input_alphabet=[04], tape_alphabet=[04, X4, _4], blank=_4, start=q04, accept=qa4, reject=qr4, transitions=[[q04, 04, q14, X4, R], [q04, _4, qr4, _4, S], [q14, _4, qa4, _4, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q04, q14, qa4, qr4], [04], [04, X4, _4], _4, q04, qa4, qr4, [[q04, _4, qr4, _4, S], [q04, 04, q14, X4, R], [q14, _4, qa4, _4, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q04, q14, qa4, qr4], [04], [04, X4, _4], _4, q04, qa4, qr4, [[q04, _4, qr4, _4, S], [q04, 04, q14, X4, R], [q14, _4, qa4, _4, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
6. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q05, q15, qa5, qr5], input_alphabet=[05], tape_alphabet=[05, X5, _5], blank=_5, start=q05, accept=qa5, reject=qr5, transitions=[[q05, 05, q15, X5, R], [q05, _5, qr5, _5, S], [q15, _5, qa5, _5, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q05, q15, qa5, qr5], [05], [05, X5, _5], _5, q05, qa5, qr5, [[q05, _5, qr5, _5, S], [q05, 05, q15, X5, R], [q15, _5, qa5, _5, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q05, q15, qa5, qr5], [05], [05, X5, _5], _5, q05, qa5, qr5, [[q05, _5, qr5, _5, S], [q05, 05, q15, X5, R], [q15, _5, qa5, _5, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
7. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q06, q16, qa6, qr6], input_alphabet=[06], tape_alphabet=[06, X6, _6], blank=_6, start=q06, accept=qa6, reject=qr6, transitions=[[q06, 06, q16, X6, R], [q06, _6, qr6, _6, S], [q16, _6, qa6, _6, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q06, q16, qa6, qr6], [06], [06, X6, _6], _6, q06, qa6, qr6, [[q06, _6, qr6, _6, S], [q06, 06, q16, X6, R], [q16, _6, qa6, _6, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q06, q16, qa6, qr6], [06], [06, X6, _6], _6, q06, qa6, qr6, [[q06, _6, qr6, _6, S], [q06, 06, q16, X6, R], [q16, _6, qa6, _6, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
8. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q07, q17, qa7, qr7], input_alphabet=[07], tape_alphabet=[07, X7, _7], blank=_7, start=q07, accept=qa7, reject=qr7, transitions=[[q07, 07, q17, X7, R], [q07, _7, qr7, _7, S], [q17, _7, qa7, _7, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q07, q17, qa7, qr7], [07], [07, X7, _7], _7, q07, qa7, qr7, [[q07, _7, qr7, _7, S], [q07, 07, q17, X7, R], [q17, _7, qa7, _7, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q07, q17, qa7, qr7], [07], [07, X7, _7], _7, q07, qa7, qr7, [[q07, _7, qr7, _7, S], [q07, 07, q17, X7, R], [q17, _7, qa7, _7, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
9. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q08, q18, qa8, qr8], input_alphabet=[08], tape_alphabet=[08, X8, _8], blank=_8, start=q08, accept=qa8, reject=qr8, transitions=[[q08, 08, q18, X8, R], [q08, _8, qr8, _8, S], [q18, _8, qa8, _8, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q08, q18, qa8, qr8], [08], [08, X8, _8], _8, q08, qa8, qr8, [[q08, _8, qr8, _8, S], [q08, 08, q18, X8, R], [q18, _8, qa8, _8, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q08, q18, qa8, qr8], [08], [08, X8, _8], _8, q08, qa8, qr8, [[q08, _8, qr8, _8, S], [q08, 08, q18, X8, R], [q18, _8, qa8, _8, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
10. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q09, q19, qa9, qr9], input_alphabet=[09], tape_alphabet=[09, X9, _9], blank=_9, start=q09, accept=qa9, reject=qr9, transitions=[[q09, 09, q19, X9, R], [q09, _9, qr9, _9, S], [q19, _9, qa9, _9, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q09, q19, qa9, qr9], [09], [09, X9, _9], _9, q09, qa9, qr9, [[q09, _9, qr9, _9, S], [q09, 09, q19, X9, R], [q19, _9, qa9, _9, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q09, q19, qa9, qr9], [09], [09, X9, _9], _9, q09, qa9, qr9, [[q09, _9, qr9, _9, S], [q09, 09, q19, X9, R], [q19, _9, qa9, _9, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
11. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q010, q110, qa10, qr10], input_alphabet=[010], tape_alphabet=[010, X10, _10], blank=_10, start=q010, accept=qa10, reject=qr10, transitions=[[q010, 010, q110, X10, R], [q010, _10, qr10, _10, S], [q110, _10, qa10, _10, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q010, q110, qa10, qr10], [010], [010, X10, _10], _10, q010, qa10, qr10, [[q010, _10, qr10, _10, S], [q010, 010, q110, X10, R], [q110, _10, qa10, _10, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q010, q110, qa10, qr10], [010], [010, X10, _10], _10, q010, qa10, qr10, [[q010, _10, qr10, _10, S], [q010, 010, q110, X10, R], [q110, _10, qa10, _10, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
12. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q011, q111, qa11, qr11], input_alphabet=[011], tape_alphabet=[011, X11, _11], blank=_11, start=q011, accept=qa11, reject=qr11, transitions=[[q011, 011, q111, X11, R], [q011, _11, qr11, _11, S], [q111, _11, qa11, _11, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q011, q111, qa11, qr11], [011], [011, X11, _11], _11, q011, qa11, qr11, [[q011, _11, qr11, _11, S], [q011, 011, q111, X11, R], [q111, _11, qa11, _11, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q011, q111, qa11, qr11], [011], [011, X11, _11], _11, q011, qa11, qr11, [[q011, _11, qr11, _11, S], [q011, 011, q111, X11, R], [q111, _11, qa11, _11, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
13. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q012, q112, qa12, qr12], input_alphabet=[012], tape_alphabet=[012, X12, _12], blank=_12, start=q012, accept=qa12, reject=qr12, transitions=[[q012, 012, q112, X12, R], [q012, _12, qr12, _12, S], [q112, _12, qa12, _12, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q012, q112, qa12, qr12], [012], [012, X12, _12], _12, q012, qa12, qr12, [[q012, _12, qr12, _12, S], [q012, 012, q112, X12, R], [q112, _12, qa12, _12, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q012, q112, qa12, qr12], [012], [012, X12, _12], _12, q012, qa12, qr12, [[q012, _12, qr12, _12, S], [q012, 012, q112, X12, R], [q112, _12, qa12, _12, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
14. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q013, q113, qa13, qr13], input_alphabet=[013], tape_alphabet=[013, X13, _13], blank=_13, start=q013, accept=qa13, reject=qr13, transitions=[[q013, 013, q113, X13, R], [q013, _13, qr13, _13, S], [q113, _13, qa13, _13, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q013, q113, qa13, qr13], [013], [013, X13, _13], _13, q013, qa13, qr13, [[q013, _13, qr13, _13, S], [q013, 013, q113, X13, R], [q113, _13, qa13, _13, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q013, q113, qa13, qr13], [013], [013, X13, _13], _13, q013, qa13, qr13, [[q013, _13, qr13, _13, S], [q013, 013, q113, X13, R], [q113, _13, qa13, _13, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
15. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q014, q114, qa14, qr14], input_alphabet=[014], tape_alphabet=[014, X14, _14], blank=_14, start=q014, accept=qa14, reject=qr14, transitions=[[q014, 014, q114, X14, R], [q014, _14, qr14, _14, S], [q114, _14, qa14, _14, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q014, q114, qa14, qr14], [014], [014, X14, _14], _14, q014, qa14, qr14, [[q014, _14, qr14, _14, S], [q014, 014, q114, X14, R], [q114, _14, qa14, _14, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q014, q114, qa14, qr14], [014], [014, X14, _14], _14, q014, qa14, qr14, [[q014, _14, qr14, _14, S], [q014, 014, q114, X14, R], [q114, _14, qa14, _14, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
16. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q015, q115, qa15, qr15], input_alphabet=[015], tape_alphabet=[015, X15, _15], blank=_15, start=q015, accept=qa15, reject=qr15, transitions=[[q015, 015, q115, X15, R], [q015, _15, qr15, _15, S], [q115, _15, qa15, _15, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q015, q115, qa15, qr15], [015], [015, X15, _15], _15, q015, qa15, qr15, [[q015, _15, qr15, _15, S], [q015, 015, q115, X15, R], [q115, _15, qa15, _15, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q015, q115, qa15, qr15], [015], [015, X15, _15], _15, q015, qa15, qr15, [[q015, _15, qr15, _15, S], [q015, 015, q115, X15, R], [q115, _15, qa15, _15, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
17. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q016, q116, qa16, qr16], input_alphabet=[016], tape_alphabet=[016, X16, _16], blank=_16, start=q016, accept=qa16, reject=qr16, transitions=[[q016, 016, q116, X16, R], [q016, _16, qr16, _16, S], [q116, _16, qa16, _16, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q016, q116, qa16, qr16], [016], [016, X16, _16], _16, q016, qa16, qr16, [[q016, _16, qr16, _16, S], [q016, 016, q116, X16, R], [q116, _16, qa16, _16, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q016, q116, qa16, qr16], [016], [016, X16, _16], _16, q016, qa16, qr16, [[q016, _16, qr16, _16, S], [q016, 016, q116, X16, R], [q116, _16, qa16, _16, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
18. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q017, q117, qa17, qr17], input_alphabet=[017], tape_alphabet=[017, X17, _17], blank=_17, start=q017, accept=qa17, reject=qr17, transitions=[[q017, 017, q117, X17, R], [q017, _17, qr17, _17, S], [q117, _17, qa17, _17, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q017, q117, qa17, qr17], [017], [017, X17, _17], _17, q017, qa17, qr17, [[q017, _17, qr17, _17, S], [q017, 017, q117, X17, R], [q117, _17, qa17, _17, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q017, q117, qa17, qr17], [017], [017, X17, _17], _17, q017, qa17, qr17, [[q017, _17, qr17, _17, S], [q017, 017, q117, X17, R], [q117, _17, qa17, _17, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
19. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q018, q118, qa18, qr18], input_alphabet=[018], tape_alphabet=[018, X18, _18], blank=_18, start=q018, accept=qa18, reject=qr18, transitions=[[q018, 018, q118, X18, R], [q018, _18, qr18, _18, S], [q118, _18, qa18, _18, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q018, q118, qa18, qr18], [018], [018, X18, _18], _18, q018, qa18, qr18, [[q018, _18, qr18, _18, S], [q018, 018, q118, X18, R], [q118, _18, qa18, _18, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q018, q118, qa18, qr18], [018], [018, X18, _18], _18, q018, qa18, qr18, [[q018, _18, qr18, _18, S], [q018, 018, q118, X18, R], [q118, _18, qa18, _18, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
20. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q019, q119, qa19, qr19], input_alphabet=[019], tape_alphabet=[019, X19, _19], blank=_19, start=q019, accept=qa19, reject=qr19, transitions=[[q019, 019, q119, X19, R], [q019, _19, qr19, _19, S], [q119, _19, qa19, _19, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q019, q119, qa19, qr19], [019], [019, X19, _19], _19, q019, qa19, qr19, [[q019, _19, qr19, _19, S], [q019, 019, q119, X19, R], [q119, _19, qa19, _19, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q019, q119, qa19, qr19], [019], [019, X19, _19], _19, q019, qa19, qr19, [[q019, _19, qr19, _19, S], [q019, 019, q119, X19, R], [q119, _19, qa19, _19, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
21. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q020, q120, qa20, qr20], input_alphabet=[020], tape_alphabet=[020, X20, _20], blank=_20, start=q020, accept=qa20, reject=qr20, transitions=[[q020, 020, q120, X20, R], [q020, _20, qr20, _20, S], [q120, _20, qa20, _20, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q020, q120, qa20, qr20], [020], [020, X20, _20], _20, q020, qa20, qr20, [[q020, _20, qr20, _20, S], [q020, 020, q120, X20, R], [q120, _20, qa20, _20, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q020, q120, qa20, qr20], [020], [020, X20, _20], _20, q020, qa20, qr20, [[q020, _20, qr20, _20, S], [q020, 020, q120, X20, R], [q120, _20, qa20, _20, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
22. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q021, q121, qa21, qr21], input_alphabet=[021], tape_alphabet=[021, X21, _21], blank=_21, start=q021, accept=qa21, reject=qr21, transitions=[[q021, 021, q121, X21, R], [q021, _21, qr21, _21, S], [q121, _21, qa21, _21, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q021, q121, qa21, qr21], [021], [021, X21, _21], _21, q021, qa21, qr21, [[q021, _21, qr21, _21, S], [q021, 021, q121, X21, R], [q121, _21, qa21, _21, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q021, q121, qa21, qr21], [021], [021, X21, _21], _21, q021, qa21, qr21, [[q021, _21, qr21, _21, S], [q021, 021, q121, X21, R], [q121, _21, qa21, _21, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
23. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q022, q122, qa22, qr22], input_alphabet=[022], tape_alphabet=[022, X22, _22], blank=_22, start=q022, accept=qa22, reject=qr22, transitions=[[q022, 022, q122, X22, R], [q022, _22, qr22, _22, S], [q122, _22, qa22, _22, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q022, q122, qa22, qr22], [022], [022, X22, _22], _22, q022, qa22, qr22, [[q022, _22, qr22, _22, S], [q022, 022, q122, X22, R], [q122, _22, qa22, _22, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q022, q122, qa22, qr22], [022], [022, X22, _22], _22, q022, qa22, qr22, [[q022, _22, qr22, _22, S], [q022, 022, q122, X22, R], [q122, _22, qa22, _22, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
24. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q023, q123, qa23, qr23], input_alphabet=[023], tape_alphabet=[023, X23, _23], blank=_23, start=q023, accept=qa23, reject=qr23, transitions=[[q023, 023, q123, X23, R], [q023, _23, qr23, _23, S], [q123, _23, qa23, _23, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q023, q123, qa23, qr23], [023], [023, X23, _23], _23, q023, qa23, qr23, [[q023, _23, qr23, _23, S], [q023, 023, q123, X23, R], [q123, _23, qa23, _23, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q023, q123, qa23, qr23], [023], [023, X23, _23], _23, q023, qa23, qr23, [[q023, _23, qr23, _23, S], [q023, 023, q123, X23, R], [q123, _23, qa23, _23, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
25. A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider
Use deterministic single-tape states=[q024, q124, qa24, qr24], input_alphabet=[024], tape_alphabet=[024, X24, _24], blank=_24, start=q024, accept=qa24, reject=qr24, transitions=[[q024, 024, q124, X24, R], [q024, _24, qr24, _24, S], [q124, _24, qa24, _24, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention).
View answer and explanation
([q024, q124, qa24, qr24], [024], [024, X24, _24], _24, q024, qa24, qr24, [[q024, _24, qr24, _24, S], [q024, 024, q124, X24, R], [q124, _24, qa24, _24, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions)
Check finite alphabets/states, blank/start/halting states, deterministic keys and every transition field. A partial transition table is permitted at signature level; absence of a rule is not silently filled with rejection. Execution and all-input total correctness remain separate. The exact result, retaining the requested order, is ([q024, q124, qa24, qr24], [024], [024, X24, _24], _24, q024, qa24, qr24, [[q024, _24, qr24, _24, S], [q024, 024, q124, X24, R], [q124, _24, qa24, _24, L]], Yes, deterministic_single_tape_signature_with_halting_states_without_outgoing_transitions).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-signature-qualification · candidate
26. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q00, q10, qa0, qr0], input_alphabet=[00], tape_alphabet=[00, X0, _0], blank=_0, start=q00, accept=qa0, reject=qr0, transitions=[[q00, 00, q10, X0, R], [q00, _0, qr0, _0, S], [q10, _0, qa0, _0, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[00], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([00], 2, [[q00, 0, [[0, 00]]], [q10, 1, [[0, X0]]], [qa0, 0, [[0, X0]]]], [step, step], qa0, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([00], 2, [[q00, 0, [[0, 00]]], [q10, 1, [[0, X0]]], [qa0, 0, [[0, X0]]]], [step, step], qa0, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
27. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q01, q11, qa1, qr1], input_alphabet=[01], tape_alphabet=[01, X1, _1], blank=_1, start=q01, accept=qa1, reject=qr1, transitions=[[q01, 01, q11, X1, R], [q01, _1, qr1, _1, S], [q11, _1, qa1, _1, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[01], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([01], 2, [[q01, 0, [[0, 01]]], [q11, 1, [[0, X1]]], [qa1, 0, [[0, X1]]]], [step, step], qa1, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([01], 2, [[q01, 0, [[0, 01]]], [q11, 1, [[0, X1]]], [qa1, 0, [[0, X1]]]], [step, step], qa1, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
28. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q02, q12, qa2, qr2], input_alphabet=[02], tape_alphabet=[02, X2, _2], blank=_2, start=q02, accept=qa2, reject=qr2, transitions=[[q02, 02, q12, X2, R], [q02, _2, qr2, _2, S], [q12, _2, qa2, _2, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[02], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([02], 2, [[q02, 0, [[0, 02]]], [q12, 1, [[0, X2]]], [qa2, 0, [[0, X2]]]], [step, step], qa2, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([02], 2, [[q02, 0, [[0, 02]]], [q12, 1, [[0, X2]]], [qa2, 0, [[0, X2]]]], [step, step], qa2, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
29. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q03, q13, qa3, qr3], input_alphabet=[03], tape_alphabet=[03, X3, _3], blank=_3, start=q03, accept=qa3, reject=qr3, transitions=[[q03, 03, q13, X3, R], [q03, _3, qr3, _3, S], [q13, _3, qa3, _3, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[03], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([03], 2, [[q03, 0, [[0, 03]]], [q13, 1, [[0, X3]]], [qa3, 0, [[0, X3]]]], [step, step], qa3, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([03], 2, [[q03, 0, [[0, 03]]], [q13, 1, [[0, X3]]], [qa3, 0, [[0, X3]]]], [step, step], qa3, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
30. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q04, q14, qa4, qr4], input_alphabet=[04], tape_alphabet=[04, X4, _4], blank=_4, start=q04, accept=qa4, reject=qr4, transitions=[[q04, 04, q14, X4, R], [q04, _4, qr4, _4, S], [q14, _4, qa4, _4, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[04], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([04], 2, [[q04, 0, [[0, 04]]], [q14, 1, [[0, X4]]], [qa4, 0, [[0, X4]]]], [step, step], qa4, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([04], 2, [[q04, 0, [[0, 04]]], [q14, 1, [[0, X4]]], [qa4, 0, [[0, X4]]]], [step, step], qa4, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
31. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q05, q15, qa5, qr5], input_alphabet=[05], tape_alphabet=[05, X5, _5], blank=_5, start=q05, accept=qa5, reject=qr5, transitions=[[q05, 05, q15, X5, R], [q05, _5, qr5, _5, S], [q15, _5, qa5, _5, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[05], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([05], 2, [[q05, 0, [[0, 05]]], [q15, 1, [[0, X5]]], [qa5, 0, [[0, X5]]]], [step, step], qa5, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([05], 2, [[q05, 0, [[0, 05]]], [q15, 1, [[0, X5]]], [qa5, 0, [[0, X5]]]], [step, step], qa5, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
32. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q06, q16, qa6, qr6], input_alphabet=[06], tape_alphabet=[06, X6, _6], blank=_6, start=q06, accept=qa6, reject=qr6, transitions=[[q06, 06, q16, X6, R], [q06, _6, qr6, _6, S], [q16, _6, qa6, _6, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[06], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([06], 2, [[q06, 0, [[0, 06]]], [q16, 1, [[0, X6]]], [qa6, 0, [[0, X6]]]], [step, step], qa6, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([06], 2, [[q06, 0, [[0, 06]]], [q16, 1, [[0, X6]]], [qa6, 0, [[0, X6]]]], [step, step], qa6, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
33. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q07, q17, qa7, qr7], input_alphabet=[07], tape_alphabet=[07, X7, _7], blank=_7, start=q07, accept=qa7, reject=qr7, transitions=[[q07, 07, q17, X7, R], [q07, _7, qr7, _7, S], [q17, _7, qa7, _7, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[07], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([07], 2, [[q07, 0, [[0, 07]]], [q17, 1, [[0, X7]]], [qa7, 0, [[0, X7]]]], [step, step], qa7, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([07], 2, [[q07, 0, [[0, 07]]], [q17, 1, [[0, X7]]], [qa7, 0, [[0, X7]]]], [step, step], qa7, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
34. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q08, q18, qa8, qr8], input_alphabet=[08], tape_alphabet=[08, X8, _8], blank=_8, start=q08, accept=qa8, reject=qr8, transitions=[[q08, 08, q18, X8, R], [q08, _8, qr8, _8, S], [q18, _8, qa8, _8, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[08], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([08], 2, [[q08, 0, [[0, 08]]], [q18, 1, [[0, X8]]], [qa8, 0, [[0, X8]]]], [step, step], qa8, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([08], 2, [[q08, 0, [[0, 08]]], [q18, 1, [[0, X8]]], [qa8, 0, [[0, X8]]]], [step, step], qa8, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
35. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q09, q19, qa9, qr9], input_alphabet=[09], tape_alphabet=[09, X9, _9], blank=_9, start=q09, accept=qa9, reject=qr9, transitions=[[q09, 09, q19, X9, R], [q09, _9, qr9, _9, S], [q19, _9, qa9, _9, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[09], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([09], 2, [[q09, 0, [[0, 09]]], [q19, 1, [[0, X9]]], [qa9, 0, [[0, X9]]]], [step, step], qa9, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([09], 2, [[q09, 0, [[0, 09]]], [q19, 1, [[0, X9]]], [qa9, 0, [[0, X9]]]], [step, step], qa9, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
36. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q010, q110, qa10, qr10], input_alphabet=[010], tape_alphabet=[010, X10, _10], blank=_10, start=q010, accept=qa10, reject=qr10, transitions=[[q010, 010, q110, X10, R], [q010, _10, qr10, _10, S], [q110, _10, qa10, _10, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[010], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([010], 2, [[q010, 0, [[0, 010]]], [q110, 1, [[0, X10]]], [qa10, 0, [[0, X10]]]], [step, step], qa10, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([010], 2, [[q010, 0, [[0, 010]]], [q110, 1, [[0, X10]]], [qa10, 0, [[0, X10]]]], [step, step], qa10, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
37. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q011, q111, qa11, qr11], input_alphabet=[011], tape_alphabet=[011, X11, _11], blank=_11, start=q011, accept=qa11, reject=qr11, transitions=[[q011, 011, q111, X11, R], [q011, _11, qr11, _11, S], [q111, _11, qa11, _11, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[011], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([011], 2, [[q011, 0, [[0, 011]]], [q111, 1, [[0, X11]]], [qa11, 0, [[0, X11]]]], [step, step], qa11, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([011], 2, [[q011, 0, [[0, 011]]], [q111, 1, [[0, X11]]], [qa11, 0, [[0, X11]]]], [step, step], qa11, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
38. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q012, q112, qa12, qr12], input_alphabet=[012], tape_alphabet=[012, X12, _12], blank=_12, start=q012, accept=qa12, reject=qr12, transitions=[[q012, 012, q112, X12, R], [q012, _12, qr12, _12, S], [q112, _12, qa12, _12, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[012], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([012], 2, [[q012, 0, [[0, 012]]], [q112, 1, [[0, X12]]], [qa12, 0, [[0, X12]]]], [step, step], qa12, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([012], 2, [[q012, 0, [[0, 012]]], [q112, 1, [[0, X12]]], [qa12, 0, [[0, X12]]]], [step, step], qa12, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
39. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q013, q113, qa13, qr13], input_alphabet=[013], tape_alphabet=[013, X13, _13], blank=_13, start=q013, accept=qa13, reject=qr13, transitions=[[q013, 013, q113, X13, R], [q013, _13, qr13, _13, S], [q113, _13, qa13, _13, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[013], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([013], 2, [[q013, 0, [[0, 013]]], [q113, 1, [[0, X13]]], [qa13, 0, [[0, X13]]]], [step, step], qa13, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([013], 2, [[q013, 0, [[0, 013]]], [q113, 1, [[0, X13]]], [qa13, 0, [[0, X13]]]], [step, step], qa13, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
40. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q014, q114, qa14, qr14], input_alphabet=[014], tape_alphabet=[014, X14, _14], blank=_14, start=q014, accept=qa14, reject=qr14, transitions=[[q014, 014, q114, X14, R], [q014, _14, qr14, _14, S], [q114, _14, qa14, _14, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[014], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([014], 2, [[q014, 0, [[0, 014]]], [q114, 1, [[0, X14]]], [qa14, 0, [[0, X14]]]], [step, step], qa14, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([014], 2, [[q014, 0, [[0, 014]]], [q114, 1, [[0, X14]]], [qa14, 0, [[0, X14]]]], [step, step], qa14, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
41. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q015, q115, qa15, qr15], input_alphabet=[015], tape_alphabet=[015, X15, _15], blank=_15, start=q015, accept=qa15, reject=qr15, transitions=[[q015, 015, q115, X15, R], [q015, _15, qr15, _15, S], [q115, _15, qa15, _15, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[015], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([015], 2, [[q015, 0, [[0, 015]]], [q115, 1, [[0, X15]]], [qa15, 0, [[0, X15]]]], [step, step], qa15, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([015], 2, [[q015, 0, [[0, 015]]], [q115, 1, [[0, X15]]], [qa15, 0, [[0, X15]]]], [step, step], qa15, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
42. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q016, q116, qa16, qr16], input_alphabet=[016], tape_alphabet=[016, X16, _16], blank=_16, start=q016, accept=qa16, reject=qr16, transitions=[[q016, 016, q116, X16, R], [q016, _16, qr16, _16, S], [q116, _16, qa16, _16, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[016], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([016], 2, [[q016, 0, [[0, 016]]], [q116, 1, [[0, X16]]], [qa16, 0, [[0, X16]]]], [step, step], qa16, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([016], 2, [[q016, 0, [[0, 016]]], [q116, 1, [[0, X16]]], [qa16, 0, [[0, X16]]]], [step, step], qa16, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
43. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q017, q117, qa17, qr17], input_alphabet=[017], tape_alphabet=[017, X17, _17], blank=_17, start=q017, accept=qa17, reject=qr17, transitions=[[q017, 017, q117, X17, R], [q017, _17, qr17, _17, S], [q117, _17, qa17, _17, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[017], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([017], 2, [[q017, 0, [[0, 017]]], [q117, 1, [[0, X17]]], [qa17, 0, [[0, X17]]]], [step, step], qa17, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([017], 2, [[q017, 0, [[0, 017]]], [q117, 1, [[0, X17]]], [qa17, 0, [[0, X17]]]], [step, step], qa17, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
44. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q018, q118, qa18, qr18], input_alphabet=[018], tape_alphabet=[018, X18, _18], blank=_18, start=q018, accept=qa18, reject=qr18, transitions=[[q018, 018, q118, X18, R], [q018, _18, qr18, _18, S], [q118, _18, qa18, _18, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[018], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([018], 2, [[q018, 0, [[0, 018]]], [q118, 1, [[0, X18]]], [qa18, 0, [[0, X18]]]], [step, step], qa18, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([018], 2, [[q018, 0, [[0, 018]]], [q118, 1, [[0, X18]]], [qa18, 0, [[0, X18]]]], [step, step], qa18, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
45. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q019, q119, qa19, qr19], input_alphabet=[019], tape_alphabet=[019, X19, _19], blank=_19, start=q019, accept=qa19, reject=qr19, transitions=[[q019, 019, q119, X19, R], [q019, _19, qr19, _19, S], [q119, _19, qa19, _19, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[019], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([019], 2, [[q019, 0, [[0, 019]]], [q119, 1, [[0, X19]]], [qa19, 0, [[0, X19]]]], [step, step], qa19, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([019], 2, [[q019, 0, [[0, 019]]], [q119, 1, [[0, X19]]], [qa19, 0, [[0, X19]]]], [step, step], qa19, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
46. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q020, q120, qa20, qr20], input_alphabet=[020], tape_alphabet=[020, X20, _20], blank=_20, start=q020, accept=qa20, reject=qr20, transitions=[[q020, 020, q120, X20, R], [q020, _20, qr20, _20, S], [q120, _20, qa20, _20, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[020], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([020], 2, [[q020, 0, [[0, 020]]], [q120, 1, [[0, X20]]], [qa20, 0, [[0, X20]]]], [step, step], qa20, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([020], 2, [[q020, 0, [[0, 020]]], [q120, 1, [[0, X20]]], [qa20, 0, [[0, X20]]]], [step, step], qa20, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
47. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q021, q121, qa21, qr21], input_alphabet=[021], tape_alphabet=[021, X21, _21], blank=_21, start=q021, accept=qa21, reject=qr21, transitions=[[q021, 021, q121, X21, R], [q021, _21, qr21, _21, S], [q121, _21, qa21, _21, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[021], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([021], 2, [[q021, 0, [[0, 021]]], [q121, 1, [[0, X21]]], [qa21, 0, [[0, X21]]]], [step, step], qa21, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([021], 2, [[q021, 0, [[0, 021]]], [q121, 1, [[0, X21]]], [qa21, 0, [[0, X21]]]], [step, step], qa21, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
48. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q022, q122, qa22, qr22], input_alphabet=[022], tape_alphabet=[022, X22, _22], blank=_22, start=q022, accept=qa22, reject=qr22, transitions=[[q022, 022, q122, X22, R], [q022, _22, qr22, _22, S], [q122, _22, qa22, _22, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[022], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([022], 2, [[q022, 0, [[0, 022]]], [q122, 1, [[0, X22]]], [qa22, 0, [[0, X22]]]], [step, step], qa22, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([022], 2, [[q022, 0, [[0, 022]]], [q122, 1, [[0, X22]]], [qa22, 0, [[0, X22]]]], [step, step], qa22, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
49. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q023, q123, qa23, qr23], input_alphabet=[023], tape_alphabet=[023, X23, _23], blank=_23, start=q023, accept=qa23, reject=qr23, transitions=[[q023, 023, q123, X23, R], [q023, _23, qr23, _23, S], [q123, _23, qa23, _23, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[023], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([023], 2, [[q023, 0, [[0, 023]]], [q123, 1, [[0, X23]]], [qa23, 0, [[0, X23]]]], [step, step], qa23, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([023], 2, [[q023, 0, [[0, 023]]], [q123, 1, [[0, X23]]], [qa23, 0, [[0, X23]]]], [step, step], qa23, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
50. A Finite Configuration Trace Has Only Its Declared Input and Budget Scope
Use deterministic single-tape states=[q024, q124, qa24, qr24], input_alphabet=[024], tape_alphabet=[024, X24, _24], blank=_24, start=q024, accept=qa24, reject=qr24, transitions=[[q024, 024, q124, X24, R], [q024, _24, qr24, _24, S], [q124, _24, qa24, _24, L]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Input=[024], step budget=2. Give (input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary).
stuck means no transition for the current read symbol, not automatic rejection. Failure to halt within a budget is not proof of an infinite loop.
View answer and explanation
([024], 2, [[q024, 0, [[0, 024]]], [q124, 1, [[0, X24]]], [qa24, 0, [[0, X24]]]], [step, step], qa24, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider)
Start at head0 with input in cells0 onward. Apply write/state/move exactly, deleting blank entries from the sparse record; stop on accept/reject, budget exhaustion or a missing rule. Missing rules produce stuck with the unchanged configuration, not automatic reject. The fixed No withholds a global decider certificate; a finite nonhalt is not an infinite-loop proof. The exact result, retaining the requested order, is ([024], 2, [[q024, 0, [[0, 024]]], [q124, 1, [[0, X24]]], [qa24, 0, [[0, X24]]]], [step, step], qa24, accept, No, finite_trace_is_input_local_and_does_not_certify_a_global_decider).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-exact-step-trace · candidate
51. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a0, b0], tape_alphabet=[a0, b0, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a0, scan, a0, R], [scan, b0, accept, b0, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b0. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a0, b0], [_, a0, b0], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a0, scan, a0, R], [scan, b0, accept, b0, S]], b0, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a0, b0], [_, a0, b0], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a0, scan, a0, R], [scan, b0, accept, b0, S]], b0, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
52. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a1, b1], tape_alphabet=[a1, b1, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a1, scan, a1, R], [scan, b1, accept, b1, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b1. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a1, b1], [_, a1, b1], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a1, scan, a1, R], [scan, b1, accept, b1, S]], b1, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a1, b1], [_, a1, b1], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a1, scan, a1, R], [scan, b1, accept, b1, S]], b1, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
53. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a2, b2], tape_alphabet=[a2, b2, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a2, scan, a2, R], [scan, b2, accept, b2, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b2. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a2, b2], [_, a2, b2], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a2, scan, a2, R], [scan, b2, accept, b2, S]], b2, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a2, b2], [_, a2, b2], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a2, scan, a2, R], [scan, b2, accept, b2, S]], b2, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
54. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a3, b3], tape_alphabet=[a3, b3, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a3, scan, a3, R], [scan, b3, accept, b3, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b3. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a3, b3], [_, a3, b3], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a3, scan, a3, R], [scan, b3, accept, b3, S]], b3, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a3, b3], [_, a3, b3], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a3, scan, a3, R], [scan, b3, accept, b3, S]], b3, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
55. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a4, b4], tape_alphabet=[a4, b4, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a4, scan, a4, R], [scan, b4, accept, b4, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b4. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a4, b4], [_, a4, b4], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a4, scan, a4, R], [scan, b4, accept, b4, S]], b4, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a4, b4], [_, a4, b4], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a4, scan, a4, R], [scan, b4, accept, b4, S]], b4, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
56. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a5, b5], tape_alphabet=[a5, b5, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a5, scan, a5, R], [scan, b5, accept, b5, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b5. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a5, b5], [_, a5, b5], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]], b5, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a5, b5], [_, a5, b5], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]], b5, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
57. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a6, b6], tape_alphabet=[a6, b6, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a6, scan, a6, R], [scan, b6, accept, b6, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b6. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a6, b6], [_, a6, b6], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a6, scan, a6, R], [scan, b6, accept, b6, S]], b6, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a6, b6], [_, a6, b6], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a6, scan, a6, R], [scan, b6, accept, b6, S]], b6, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
58. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a7, b7], tape_alphabet=[a7, b7, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a7, scan, a7, R], [scan, b7, accept, b7, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b7. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a7, b7], [_, a7, b7], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a7, scan, a7, R], [scan, b7, accept, b7, S]], b7, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a7, b7], [_, a7, b7], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a7, scan, a7, R], [scan, b7, accept, b7, S]], b7, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
59. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a8, b8], tape_alphabet=[a8, b8, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a8, scan, a8, R], [scan, b8, accept, b8, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b8. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a8, b8], [_, a8, b8], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a8, scan, a8, R], [scan, b8, accept, b8, S]], b8, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a8, b8], [_, a8, b8], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a8, scan, a8, R], [scan, b8, accept, b8, S]], b8, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
60. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a9, b9], tape_alphabet=[a9, b9, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a9, scan, a9, R], [scan, b9, accept, b9, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b9. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a9, b9], [_, a9, b9], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]], b9, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a9, b9], [_, a9, b9], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]], b9, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
61. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a10, b10], tape_alphabet=[a10, b10, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a10, scan, a10, R], [scan, b10, accept, b10, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b10. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a10, b10], [_, a10, b10], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], b10, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a10, b10], [_, a10, b10], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], b10, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
62. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a11, b11], tape_alphabet=[a11, b11, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a11, scan, a11, R], [scan, b11, accept, b11, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b11. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a11, b11], [_, a11, b11], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]], b11, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a11, b11], [_, a11, b11], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]], b11, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
63. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a12, b12], tape_alphabet=[a12, b12, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a12, scan, a12, R], [scan, b12, accept, b12, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b12. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a12, b12], [_, a12, b12], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]], b12, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a12, b12], [_, a12, b12], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]], b12, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
64. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a13, b13], tape_alphabet=[a13, b13, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a13, scan, a13, R], [scan, b13, accept, b13, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b13. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a13, b13], [_, a13, b13], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a13, scan, a13, R], [scan, b13, accept, b13, S]], b13, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a13, b13], [_, a13, b13], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a13, scan, a13, R], [scan, b13, accept, b13, S]], b13, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
65. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a14, b14], tape_alphabet=[a14, b14, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a14, scan, a14, R], [scan, b14, accept, b14, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b14. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a14, b14], [_, a14, b14], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a14, scan, a14, R], [scan, b14, accept, b14, S]], b14, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a14, b14], [_, a14, b14], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a14, scan, a14, R], [scan, b14, accept, b14, S]], b14, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
66. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a15, b15], tape_alphabet=[a15, b15, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a15, scan, a15, R], [scan, b15, accept, b15, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b15. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a15, b15], [_, a15, b15], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a15, scan, a15, R], [scan, b15, accept, b15, S]], b15, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a15, b15], [_, a15, b15], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a15, scan, a15, R], [scan, b15, accept, b15, S]], b15, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
67. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a16, b16], tape_alphabet=[a16, b16, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a16, scan, a16, R], [scan, b16, accept, b16, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b16. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a16, b16], [_, a16, b16], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]], b16, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a16, b16], [_, a16, b16], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]], b16, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
68. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a17, b17], tape_alphabet=[a17, b17, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a17, scan, a17, R], [scan, b17, accept, b17, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b17. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a17, b17], [_, a17, b17], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a17, scan, a17, R], [scan, b17, accept, b17, S]], b17, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a17, b17], [_, a17, b17], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a17, scan, a17, R], [scan, b17, accept, b17, S]], b17, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
69. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a18, b18], tape_alphabet=[a18, b18, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a18, scan, a18, R], [scan, b18, accept, b18, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b18. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a18, b18], [_, a18, b18], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a18, scan, a18, R], [scan, b18, accept, b18, S]], b18, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a18, b18], [_, a18, b18], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a18, scan, a18, R], [scan, b18, accept, b18, S]], b18, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
70. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a19, b19], tape_alphabet=[a19, b19, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a19, scan, a19, R], [scan, b19, accept, b19, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b19. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a19, b19], [_, a19, b19], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a19, scan, a19, R], [scan, b19, accept, b19, S]], b19, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a19, b19], [_, a19, b19], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a19, scan, a19, R], [scan, b19, accept, b19, S]], b19, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
71. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a20, b20], tape_alphabet=[a20, b20, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a20, scan, a20, R], [scan, b20, accept, b20, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b20. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a20, b20], [_, a20, b20], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a20, scan, a20, R], [scan, b20, accept, b20, S]], b20, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a20, b20], [_, a20, b20], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a20, scan, a20, R], [scan, b20, accept, b20, S]], b20, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
72. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a21, b21], tape_alphabet=[a21, b21, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a21, scan, a21, R], [scan, b21, accept, b21, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b21. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a21, b21], [_, a21, b21], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a21, scan, a21, R], [scan, b21, accept, b21, S]], b21, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a21, b21], [_, a21, b21], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a21, scan, a21, R], [scan, b21, accept, b21, S]], b21, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
73. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a22, b22], tape_alphabet=[a22, b22, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a22, scan, a22, R], [scan, b22, accept, b22, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b22. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a22, b22], [_, a22, b22], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a22, scan, a22, R], [scan, b22, accept, b22, S]], b22, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a22, b22], [_, a22, b22], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a22, scan, a22, R], [scan, b22, accept, b22, S]], b22, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
74. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a23, b23], tape_alphabet=[a23, b23, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a23, scan, a23, R], [scan, b23, accept, b23, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b23. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a23, b23], [_, a23, b23], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a23, scan, a23, R], [scan, b23, accept, b23, S]], b23, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a23, b23], [_, a23, b23], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a23, scan, a23, R], [scan, b23, accept, b23, S]], b23, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
75. A Canonical Scan Schema Has an All-Input Ranking and Correct Answers
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a24, b24], tape_alphabet=[a24, b24, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a24, scan, a24, R], [scan, b24, accept, b24, S], [scan, _, reject, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target input symbol=b24. Give (states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, target_symbol, ranking, decrease_rule, step_bound, schema_decider_certificate, certificate).
View answer and explanation
([accept, reject, scan], [a24, b24], [_, a24, b24], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a24, scan, a24, R], [scan, b24, accept, b24, S]], b24, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words)
Require the exact canonical schema: copy and move right on nontarget symbols, accept on the target, reject on blank. For every legal word w, unscanned input cells plus1 decreases on scanning; assign rank0 after halting, including the final accept/reject step. The bound is |w|+1 and the answer is correct for the language containing the target. This pattern-bound certificate does not certify arbitrary machines from sample traces. The exact result, retaining the requested order, is ([accept, reject, scan], [a24, b24], [_, a24, b24], _, scan, accept, reject, [[scan, _, reject, _, S], [scan, a24, scan, a24, R], [scan, b24, accept, b24, S]], b24, ranking=unscanned_input_cells_plus_one, strictly_decreases_on_every_scan_step, |w|+1, Yes, global_termination_and_answer_correctness_certificate_for_all_words).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-global-decider-ranking · candidate
76. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a0, b0], tape_alphabet=[a0, b0, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a0, scan, a0, R], [scan, b0, accept, b0, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b0, legal target-free input=[a0, a0]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a0, b0], [_, a0, b0], [[scan, _, scan, _, S], [scan, a0, scan, a0, R], [scan, b0, accept, b0, S]], b0, [a0, a0], [scan, 2, [[0, a0], [1, a0]]], [scan, 2, [[0, a0], [1, a0]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a0, b0], [_, a0, b0], [[scan, _, scan, _, S], [scan, a0, scan, a0, R], [scan, b0, accept, b0, S]], b0, [a0, a0], [scan, 2, [[0, a0], [1, a0]]], [scan, 2, [[0, a0], [1, a0]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
77. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a1, b1], tape_alphabet=[a1, b1, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a1, scan, a1, R], [scan, b1, accept, b1, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b1, legal target-free input=[a1, a1]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a1, b1], [_, a1, b1], [[scan, _, scan, _, S], [scan, a1, scan, a1, R], [scan, b1, accept, b1, S]], b1, [a1, a1], [scan, 2, [[0, a1], [1, a1]]], [scan, 2, [[0, a1], [1, a1]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a1, b1], [_, a1, b1], [[scan, _, scan, _, S], [scan, a1, scan, a1, R], [scan, b1, accept, b1, S]], b1, [a1, a1], [scan, 2, [[0, a1], [1, a1]]], [scan, 2, [[0, a1], [1, a1]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
78. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a2, b2], tape_alphabet=[a2, b2, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a2, scan, a2, R], [scan, b2, accept, b2, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b2, legal target-free input=[a2, a2]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a2, b2], [_, a2, b2], [[scan, _, scan, _, S], [scan, a2, scan, a2, R], [scan, b2, accept, b2, S]], b2, [a2, a2], [scan, 2, [[0, a2], [1, a2]]], [scan, 2, [[0, a2], [1, a2]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a2, b2], [_, a2, b2], [[scan, _, scan, _, S], [scan, a2, scan, a2, R], [scan, b2, accept, b2, S]], b2, [a2, a2], [scan, 2, [[0, a2], [1, a2]]], [scan, 2, [[0, a2], [1, a2]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
79. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a3, b3], tape_alphabet=[a3, b3, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a3, scan, a3, R], [scan, b3, accept, b3, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b3, legal target-free input=[a3, a3]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a3, b3], [_, a3, b3], [[scan, _, scan, _, S], [scan, a3, scan, a3, R], [scan, b3, accept, b3, S]], b3, [a3, a3], [scan, 2, [[0, a3], [1, a3]]], [scan, 2, [[0, a3], [1, a3]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a3, b3], [_, a3, b3], [[scan, _, scan, _, S], [scan, a3, scan, a3, R], [scan, b3, accept, b3, S]], b3, [a3, a3], [scan, 2, [[0, a3], [1, a3]]], [scan, 2, [[0, a3], [1, a3]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
80. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a4, b4], tape_alphabet=[a4, b4, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a4, scan, a4, R], [scan, b4, accept, b4, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b4, legal target-free input=[a4, a4]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a4, b4], [_, a4, b4], [[scan, _, scan, _, S], [scan, a4, scan, a4, R], [scan, b4, accept, b4, S]], b4, [a4, a4], [scan, 2, [[0, a4], [1, a4]]], [scan, 2, [[0, a4], [1, a4]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a4, b4], [_, a4, b4], [[scan, _, scan, _, S], [scan, a4, scan, a4, R], [scan, b4, accept, b4, S]], b4, [a4, a4], [scan, 2, [[0, a4], [1, a4]]], [scan, 2, [[0, a4], [1, a4]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
81. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a5, b5], tape_alphabet=[a5, b5, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a5, scan, a5, R], [scan, b5, accept, b5, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b5, legal target-free input=[a5, a5]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a5, b5], [_, a5, b5], [[scan, _, scan, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]], b5, [a5, a5], [scan, 2, [[0, a5], [1, a5]]], [scan, 2, [[0, a5], [1, a5]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a5, b5], [_, a5, b5], [[scan, _, scan, _, S], [scan, a5, scan, a5, R], [scan, b5, accept, b5, S]], b5, [a5, a5], [scan, 2, [[0, a5], [1, a5]]], [scan, 2, [[0, a5], [1, a5]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
82. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a6, b6], tape_alphabet=[a6, b6, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a6, scan, a6, R], [scan, b6, accept, b6, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b6, legal target-free input=[a6, a6]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a6, b6], [_, a6, b6], [[scan, _, scan, _, S], [scan, a6, scan, a6, R], [scan, b6, accept, b6, S]], b6, [a6, a6], [scan, 2, [[0, a6], [1, a6]]], [scan, 2, [[0, a6], [1, a6]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a6, b6], [_, a6, b6], [[scan, _, scan, _, S], [scan, a6, scan, a6, R], [scan, b6, accept, b6, S]], b6, [a6, a6], [scan, 2, [[0, a6], [1, a6]]], [scan, 2, [[0, a6], [1, a6]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
83. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a7, b7], tape_alphabet=[a7, b7, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a7, scan, a7, R], [scan, b7, accept, b7, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b7, legal target-free input=[a7, a7]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a7, b7], [_, a7, b7], [[scan, _, scan, _, S], [scan, a7, scan, a7, R], [scan, b7, accept, b7, S]], b7, [a7, a7], [scan, 2, [[0, a7], [1, a7]]], [scan, 2, [[0, a7], [1, a7]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a7, b7], [_, a7, b7], [[scan, _, scan, _, S], [scan, a7, scan, a7, R], [scan, b7, accept, b7, S]], b7, [a7, a7], [scan, 2, [[0, a7], [1, a7]]], [scan, 2, [[0, a7], [1, a7]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
84. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a8, b8], tape_alphabet=[a8, b8, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a8, scan, a8, R], [scan, b8, accept, b8, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b8, legal target-free input=[a8, a8]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a8, b8], [_, a8, b8], [[scan, _, scan, _, S], [scan, a8, scan, a8, R], [scan, b8, accept, b8, S]], b8, [a8, a8], [scan, 2, [[0, a8], [1, a8]]], [scan, 2, [[0, a8], [1, a8]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a8, b8], [_, a8, b8], [[scan, _, scan, _, S], [scan, a8, scan, a8, R], [scan, b8, accept, b8, S]], b8, [a8, a8], [scan, 2, [[0, a8], [1, a8]]], [scan, 2, [[0, a8], [1, a8]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
85. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a9, b9], tape_alphabet=[a9, b9, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a9, scan, a9, R], [scan, b9, accept, b9, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b9, legal target-free input=[a9, a9]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a9, b9], [_, a9, b9], [[scan, _, scan, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]], b9, [a9, a9], [scan, 2, [[0, a9], [1, a9]]], [scan, 2, [[0, a9], [1, a9]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a9, b9], [_, a9, b9], [[scan, _, scan, _, S], [scan, a9, scan, a9, R], [scan, b9, accept, b9, S]], b9, [a9, a9], [scan, 2, [[0, a9], [1, a9]]], [scan, 2, [[0, a9], [1, a9]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
86. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a10, b10], tape_alphabet=[a10, b10, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a10, scan, a10, R], [scan, b10, accept, b10, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b10, legal target-free input=[a10, a10]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a10, b10], [_, a10, b10], [[scan, _, scan, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], b10, [a10, a10], [scan, 2, [[0, a10], [1, a10]]], [scan, 2, [[0, a10], [1, a10]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a10, b10], [_, a10, b10], [[scan, _, scan, _, S], [scan, a10, scan, a10, R], [scan, b10, accept, b10, S]], b10, [a10, a10], [scan, 2, [[0, a10], [1, a10]]], [scan, 2, [[0, a10], [1, a10]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
87. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a11, b11], tape_alphabet=[a11, b11, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a11, scan, a11, R], [scan, b11, accept, b11, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b11, legal target-free input=[a11, a11]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a11, b11], [_, a11, b11], [[scan, _, scan, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]], b11, [a11, a11], [scan, 2, [[0, a11], [1, a11]]], [scan, 2, [[0, a11], [1, a11]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a11, b11], [_, a11, b11], [[scan, _, scan, _, S], [scan, a11, scan, a11, R], [scan, b11, accept, b11, S]], b11, [a11, a11], [scan, 2, [[0, a11], [1, a11]]], [scan, 2, [[0, a11], [1, a11]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
88. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a12, b12], tape_alphabet=[a12, b12, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a12, scan, a12, R], [scan, b12, accept, b12, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b12, legal target-free input=[a12, a12]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a12, b12], [_, a12, b12], [[scan, _, scan, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]], b12, [a12, a12], [scan, 2, [[0, a12], [1, a12]]], [scan, 2, [[0, a12], [1, a12]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a12, b12], [_, a12, b12], [[scan, _, scan, _, S], [scan, a12, scan, a12, R], [scan, b12, accept, b12, S]], b12, [a12, a12], [scan, 2, [[0, a12], [1, a12]]], [scan, 2, [[0, a12], [1, a12]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
89. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a13, b13], tape_alphabet=[a13, b13, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a13, scan, a13, R], [scan, b13, accept, b13, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b13, legal target-free input=[a13, a13]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a13, b13], [_, a13, b13], [[scan, _, scan, _, S], [scan, a13, scan, a13, R], [scan, b13, accept, b13, S]], b13, [a13, a13], [scan, 2, [[0, a13], [1, a13]]], [scan, 2, [[0, a13], [1, a13]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a13, b13], [_, a13, b13], [[scan, _, scan, _, S], [scan, a13, scan, a13, R], [scan, b13, accept, b13, S]], b13, [a13, a13], [scan, 2, [[0, a13], [1, a13]]], [scan, 2, [[0, a13], [1, a13]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
90. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a14, b14], tape_alphabet=[a14, b14, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a14, scan, a14, R], [scan, b14, accept, b14, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b14, legal target-free input=[a14, a14]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a14, b14], [_, a14, b14], [[scan, _, scan, _, S], [scan, a14, scan, a14, R], [scan, b14, accept, b14, S]], b14, [a14, a14], [scan, 2, [[0, a14], [1, a14]]], [scan, 2, [[0, a14], [1, a14]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a14, b14], [_, a14, b14], [[scan, _, scan, _, S], [scan, a14, scan, a14, R], [scan, b14, accept, b14, S]], b14, [a14, a14], [scan, 2, [[0, a14], [1, a14]]], [scan, 2, [[0, a14], [1, a14]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
91. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a15, b15], tape_alphabet=[a15, b15, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a15, scan, a15, R], [scan, b15, accept, b15, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b15, legal target-free input=[a15, a15]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a15, b15], [_, a15, b15], [[scan, _, scan, _, S], [scan, a15, scan, a15, R], [scan, b15, accept, b15, S]], b15, [a15, a15], [scan, 2, [[0, a15], [1, a15]]], [scan, 2, [[0, a15], [1, a15]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a15, b15], [_, a15, b15], [[scan, _, scan, _, S], [scan, a15, scan, a15, R], [scan, b15, accept, b15, S]], b15, [a15, a15], [scan, 2, [[0, a15], [1, a15]]], [scan, 2, [[0, a15], [1, a15]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
92. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a16, b16], tape_alphabet=[a16, b16, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a16, scan, a16, R], [scan, b16, accept, b16, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b16, legal target-free input=[a16, a16]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a16, b16], [_, a16, b16], [[scan, _, scan, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]], b16, [a16, a16], [scan, 2, [[0, a16], [1, a16]]], [scan, 2, [[0, a16], [1, a16]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a16, b16], [_, a16, b16], [[scan, _, scan, _, S], [scan, a16, scan, a16, R], [scan, b16, accept, b16, S]], b16, [a16, a16], [scan, 2, [[0, a16], [1, a16]]], [scan, 2, [[0, a16], [1, a16]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
93. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a17, b17], tape_alphabet=[a17, b17, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a17, scan, a17, R], [scan, b17, accept, b17, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b17, legal target-free input=[a17, a17]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a17, b17], [_, a17, b17], [[scan, _, scan, _, S], [scan, a17, scan, a17, R], [scan, b17, accept, b17, S]], b17, [a17, a17], [scan, 2, [[0, a17], [1, a17]]], [scan, 2, [[0, a17], [1, a17]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a17, b17], [_, a17, b17], [[scan, _, scan, _, S], [scan, a17, scan, a17, R], [scan, b17, accept, b17, S]], b17, [a17, a17], [scan, 2, [[0, a17], [1, a17]]], [scan, 2, [[0, a17], [1, a17]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
94. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a18, b18], tape_alphabet=[a18, b18, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a18, scan, a18, R], [scan, b18, accept, b18, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b18, legal target-free input=[a18, a18]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a18, b18], [_, a18, b18], [[scan, _, scan, _, S], [scan, a18, scan, a18, R], [scan, b18, accept, b18, S]], b18, [a18, a18], [scan, 2, [[0, a18], [1, a18]]], [scan, 2, [[0, a18], [1, a18]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a18, b18], [_, a18, b18], [[scan, _, scan, _, S], [scan, a18, scan, a18, R], [scan, b18, accept, b18, S]], b18, [a18, a18], [scan, 2, [[0, a18], [1, a18]]], [scan, 2, [[0, a18], [1, a18]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
95. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a19, b19], tape_alphabet=[a19, b19, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a19, scan, a19, R], [scan, b19, accept, b19, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b19, legal target-free input=[a19, a19]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a19, b19], [_, a19, b19], [[scan, _, scan, _, S], [scan, a19, scan, a19, R], [scan, b19, accept, b19, S]], b19, [a19, a19], [scan, 2, [[0, a19], [1, a19]]], [scan, 2, [[0, a19], [1, a19]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a19, b19], [_, a19, b19], [[scan, _, scan, _, S], [scan, a19, scan, a19, R], [scan, b19, accept, b19, S]], b19, [a19, a19], [scan, 2, [[0, a19], [1, a19]]], [scan, 2, [[0, a19], [1, a19]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
96. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a20, b20], tape_alphabet=[a20, b20, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a20, scan, a20, R], [scan, b20, accept, b20, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b20, legal target-free input=[a20, a20]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a20, b20], [_, a20, b20], [[scan, _, scan, _, S], [scan, a20, scan, a20, R], [scan, b20, accept, b20, S]], b20, [a20, a20], [scan, 2, [[0, a20], [1, a20]]], [scan, 2, [[0, a20], [1, a20]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a20, b20], [_, a20, b20], [[scan, _, scan, _, S], [scan, a20, scan, a20, R], [scan, b20, accept, b20, S]], b20, [a20, a20], [scan, 2, [[0, a20], [1, a20]]], [scan, 2, [[0, a20], [1, a20]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
97. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a21, b21], tape_alphabet=[a21, b21, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a21, scan, a21, R], [scan, b21, accept, b21, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b21, legal target-free input=[a21, a21]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a21, b21], [_, a21, b21], [[scan, _, scan, _, S], [scan, a21, scan, a21, R], [scan, b21, accept, b21, S]], b21, [a21, a21], [scan, 2, [[0, a21], [1, a21]]], [scan, 2, [[0, a21], [1, a21]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a21, b21], [_, a21, b21], [[scan, _, scan, _, S], [scan, a21, scan, a21, R], [scan, b21, accept, b21, S]], b21, [a21, a21], [scan, 2, [[0, a21], [1, a21]]], [scan, 2, [[0, a21], [1, a21]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
98. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a22, b22], tape_alphabet=[a22, b22, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a22, scan, a22, R], [scan, b22, accept, b22, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b22, legal target-free input=[a22, a22]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a22, b22], [_, a22, b22], [[scan, _, scan, _, S], [scan, a22, scan, a22, R], [scan, b22, accept, b22, S]], b22, [a22, a22], [scan, 2, [[0, a22], [1, a22]]], [scan, 2, [[0, a22], [1, a22]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a22, b22], [_, a22, b22], [[scan, _, scan, _, S], [scan, a22, scan, a22, R], [scan, b22, accept, b22, S]], b22, [a22, a22], [scan, 2, [[0, a22], [1, a22]]], [scan, 2, [[0, a22], [1, a22]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
99. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a23, b23], tape_alphabet=[a23, b23, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a23, scan, a23, R], [scan, b23, accept, b23, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b23, legal target-free input=[a23, a23]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a23, b23], [_, a23, b23], [[scan, _, scan, _, S], [scan, a23, scan, a23, R], [scan, b23, accept, b23, S]], b23, [a23, a23], [scan, 2, [[0, a23], [1, a23]]], [scan, 2, [[0, a23], [1, a23]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a23, b23], [_, a23, b23], [[scan, _, scan, _, S], [scan, a23, scan, a23, R], [scan, b23, accept, b23, S]], b23, [a23, a23], [scan, 2, [[0, a23], [1, a23]]], [scan, 2, [[0, a23], [1, a23]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
100. An Explicit Repeated Blank Configuration Proves This Recognizer Is Not a Decider
Use deterministic single-tape states=[scan, accept, reject], input_alphabet=[a24, b24], tape_alphabet=[a24, b24, _], blank=_, start=scan, accept=accept, reject=reject, transitions=[[scan, a24, scan, a24, R], [scan, b24, accept, b24, S], [scan, _, scan, _, S]]. Each transition is [state,read,next,write,L/R/S]; keys [state,read] are unique and halting states have no outgoing transitions. Input symbols form a blank-free tape subset. The integer-indexed tape is blank at every unlisted cell, with configuration [state,head,sparse nonblank tape]; L may move left of0. Canonical answer transitions/tape cells retain the source sort convention. Target=b24, legal target-free input=[a24, a24]. Give (states, input_alphabet, tape_alphabet, transitions, target_symbol, input, loop_configuration, next_configuration, exact_self_loop, decider, boundary).
View answer and explanation
([accept, reject, scan], [a24, b24], [_, a24, b24], [[scan, _, scan, _, S], [scan, a24, scan, a24, R], [scan, b24, accept, b24, S]], b24, [a24, a24], [scan, 2, [[0, a24], [1, a24]]], [scan, 2, [[0, a24], [1, a24]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input)
Require the canonical recognizer schema that loops in scan on blank without moving or changing tape. After all nontarget input cells are scanned, the exact blank configuration repeats forever. This is a constructive nontermination witness for that input, stronger than bounded simulation failure; it does not claim every recognizer fails to be a decider. The exact result, retaining the requested order, is ([accept, reject, scan], [a24, b24], [_, a24, b24], [[scan, _, scan, _, S], [scan, a24, scan, a24, R], [scan, b24, accept, b24, S]], b24, [a24, a24], [scan, 2, [[0, a24], [1, a24]]], [scan, 2, [[0, a24], [1, a24]]], Yes, No, explicit_blank_self_loop_proves_this_recognizer_is_not_a_decider_on_the_target_free_input).
Reviewed step-by-step derivation
Turing-machine decision model · qf-mod44-tm-recognizer-loop-boundary · candidate
Canonical question JSONL · English JSONL · Validation report