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Question 8721: Whole Finite Decider Table against Its Specification

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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R0016-08721 · q-20261013-advance-20261018-r06-decision-problem-0046

Original question and givens

The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

  • G001 — The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [2, 4], normalized as a set. The specification is separate from the supplied Boolean decider table; finite table agreement implies no general infinite-domain decidability result. Complete decider=[false, false, true, false, true, false]. Give (n, yes-instance set, decider values, all mismatch indices, complete agreement?).

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=[2, 4]

After

normalized yes set=[2, 4]

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;spec=No;declared decider=No

After

mismatch=No

Conditions: none

Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.

Step identifiers and dependencies

Rule: finite_decision_each_decider_cell · Uses: G001, S001

S003 · implies

Before

input=1;spec=No;declared decider=No

After

mismatch=No

Conditions: none

Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.

Step identifiers and dependencies

Rule: finite_decision_each_decider_cell · Uses: G001, S002

S004 · implies

Before

input=2;spec=Yes;declared decider=Yes

After

mismatch=No

Conditions: none

Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.

Step identifiers and dependencies

Rule: finite_decision_each_decider_cell · Uses: G001, S003

S005 · implies

Before

input=3;spec=No;declared decider=No

After

mismatch=No

Conditions: none

Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.

Step identifiers and dependencies

Rule: finite_decision_each_decider_cell · Uses: G001, S004

S006 · implies

Before

input=4;spec=Yes;declared decider=Yes

After

mismatch=No

Conditions: none

Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.

Step identifiers and dependencies

Rule: finite_decision_each_decider_cell · Uses: G001, S005

S007 · implies

Before

input=5;spec=No;declared decider=No

After

mismatch=No

Conditions: none

Compare specification and decider at the same original input,checking every cell.The decider does not define its own correctness.

Step identifiers and dependencies

Rule: finite_decision_each_decider_cell · Uses: G001, S006

S008 · implies

Before

complete mismatch labels=[]

After

complete agreement=Yes

Conditions: none

Complete agreement means no mismatch anywhere in the finite domain;the condition holds vacuously on an empty domain.

Step identifiers and dependencies

Rule: complete_decision_agreement_gate · Uses: G001, S007

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 — 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, [2, 4], [No, No, Yes, No, Yes, No], [], Yes)

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: 57e334087bb038459b134f51f90e811648758a0c0340db692253758749dfa7d3
  • candidate record SHA-256: 642204a12eeeb90d907677209cc42dde4aa003e426d93e7b12a891c021d4fc2d
  • semantic review receipt SHA-256: 00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2
  • question-first witness SHA-256: 198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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