Question 24778: A Qualified Deterministic Single-Tape Signature Is Not Yet a Global Decider

Original question and givens

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).

• G001 — 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).

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 = [[q02, q12, qa2, qr2], [02], [02, X2, _2], _2, q02, qa2, qr2, [[q02, 02, q12, X2, R], [q02, _2, qr2, _2, S], [q12, _2, qa2, _2, L]]]

derived = [[q02, q12, qa2, qr2], [02], [02, X2, _2], [[q02, _2, qr2, _2, S], [q02, 02, q12, X2, R], [q12, _2, qa2, _2, 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

([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)

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.