Question 24720: A Finite Configuration Trace Has Only Its Declared Input and Budget Scope

Original question and givens

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).

• G001 — 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).

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 = [[q019, q119, qa19, qr19], [019], [019, X19, _19], _19, q019, qa19, qr19, [[q019, 019, q119, X19, R], [q019, _19, qr19, _19, S], [q119, _19, qa19, _19, L]]]

derived = [[q019, q119, qa19, qr19], [019], [019, X19, _19], [[q019, _19, qr19, _19, S], [q019, 019, q119, X19, R], [q119, _19, qa19, _19, L]], Yes]

source roles = [[019], q019, _19]

derived = [[q019, 0, [[0, 019]]]]

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

TM exact integer head move0 = 1

source roles = [0, [q019, 0, [[0, 019]]], 019, [q019, 019, q119, X19, R]]

derived = [step, [q119, 1, [[0, X19]]]]

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

TM exact integer head move1 = 0

source roles = [1, [q119, 1, [[0, X19]]], _19, [q119, _19, qa19, _19, L]]

derived = [step, [qa19, 0, [[0, X19]]]]

source roles = [[019], 2, [[q019, 0, [[0, 019]]], [q119, 1, [[0, X19]]], [qa19, 0, [[0, X19]]]], [step, step]]

derived = [qa19, 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

([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)

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.