Question 24777: A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider

Original question and givens

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).

• G001 — 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).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-turing-machine-decision-model

Step-by-step derivation

source roles = [tm-signature-qualification]

derived = [[states, input_alphabet, tape_alphabet, blank, start, accept, reject, transitions, qualified, convention]]

source roles = [[q01, q11, qa1, qr1], [01], [01, X1, _1], _1, q01, qa1, qr1, [[q01, 01, q11, X1, R], [q01, _1, qr1, _1, S], [q11, _1, qa1, _1, L]]]

derived = [[q01, q11, qa1, qr1], [01], [01, X1, _1], [[q01, _1, qr1, _1, S], [q01, 01, q11, X1, R], [q11, _1, qa1, _1, L]], Yes]

Reverse checks

• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

([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)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.