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Question 8762: Finite Decision Specification and Complete Truth Table

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0016-08762 · q-20261013-advance-20261018-r06-decision-problem-0012

Original question and givens

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

  • G001 — The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [0, 1, 3], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Give (n, normalized yes-instance set, complete indexed truth table).

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.

Step-by-step derivation

S001 · implies

Before

domain Fin(6);raw yes instances=[0, 1, 3]

After

normalized yes set=[0, 1, 3]

Conditions: none

Keep the yes-instance specification separate from the candidate decider.Deduplicate labels as a set and reject outside-domain labels.A complete finite table does not prove an arbitrary program decidable or terminating on infinite inputs.

Step identifiers and dependencies

Rule: finite_decision_spec_not_program_execution · Uses: G001

S002 · implies

Before

input=0;yes set=[0, 1, 3]

After

specification value=Yes

Conditions: none

Use membership in the specification yes set for this cell,retaining every legal input.

Step identifiers and dependencies

Rule: finite_decision_complete_spec_cell · Uses: G001, S001

S003 · implies

Before

input=1;yes set=[0, 1, 3]

After

specification value=Yes

Conditions: none

Use membership in the specification yes set for this cell,retaining every legal input.

Step identifiers and dependencies

Rule: finite_decision_complete_spec_cell · Uses: G001, S002

S004 · implies

Before

input=2;yes set=[0, 1, 3]

After

specification value=No

Conditions: none

Use membership in the specification yes set for this cell,retaining every legal input.

Step identifiers and dependencies

Rule: finite_decision_complete_spec_cell · Uses: G001, S003

S005 · implies

Before

input=3;yes set=[0, 1, 3]

After

specification value=Yes

Conditions: none

Use membership in the specification yes set for this cell,retaining every legal input.

Step identifiers and dependencies

Rule: finite_decision_complete_spec_cell · Uses: G001, S004

S006 · implies

Before

input=4;yes set=[0, 1, 3]

After

specification value=No

Conditions: none

Use membership in the specification yes set for this cell,retaining every legal input.

Step identifiers and dependencies

Rule: finite_decision_complete_spec_cell · Uses: G001, S005

S007 · implies

Before

input=5;yes set=[0, 1, 3]

After

specification value=No

Conditions: none

Use membership in the specification yes set for this cell,retaining every legal input.

Step identifiers and dependencies

Rule: finite_decision_complete_spec_cell · Uses: G001, S006

Reverse checks

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

(6, [0, 1, 3], [[0, Yes], [1, Yes], [2, No], [3, Yes], [4, No], [5, No]])

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 75c1dfe28dbfb4e18a6f845dc2b27898ab4869a4d8ad25cc838065f5b573fe49
  • candidate record SHA-256: b4910edf602bf834bd5e912e51b9d2d73fbe1c2a3ba684bbeea26bf9d583a2d2
  • semantic review receipt SHA-256: 00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2
  • question-first witness SHA-256: 198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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