Question 24711: A Finite Configuration Trace Has Only Its Declared Input and Budget Scope

Original question and givens

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).

• G001 — 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).

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-exact-step-trace]

derived = [[input, step_budget, configurations, step_outcomes, final_state, local_outcome, global_decider_certificate, boundary]]

source roles = [[q010, q110, qa10, qr10], [010], [010, X10, _10], _10, q010, qa10, qr10, [[q010, 010, q110, X10, R], [q010, _10, qr10, _10, S], [q110, _10, qa10, _10, L]]]

derived = [[q010, q110, qa10, qr10], [010], [010, X10, _10], [[q010, _10, qr10, _10, S], [q010, 010, q110, X10, R], [q110, _10, qa10, _10, L]], Yes]

source roles = [[010], q010, _10]

derived = [[q010, 0, [[0, 010]]]]

TM exact integer head move0 := sum(0, 1)

TM exact integer head move0 = 1

source roles = [0, [q010, 0, [[0, 010]]], 010, [q010, 010, q110, X10, R]]

derived = [step, [q110, 1, [[0, X10]]]]

TM exact integer head move1 := sum(1, -1)

TM exact integer head move1 = 0

source roles = [1, [q110, 1, [[0, X10]]], _10, [q110, _10, qa10, _10, L]]

derived = [step, [qa10, 0, [[0, X10]]]]

source roles = [[010], 2, [[q010, 0, [[0, 010]]], [q110, 1, [[0, X10]]], [qa10, 0, [[0, X10]]]], [step, step]]

derived = [qa10, accept, No]

Reverse checks

• S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S006 · premise_and_result_audit — Recompute TM exact integer head move1 with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S004 · premise_and_result_audit — Recompute TM exact integer head move0 with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• 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

([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)

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.