# Question 8775: Finite Decision Specification and Complete Truth Table [Return to catalogue page 44](https://ocme.evemisslab.com/en/questions/page/44/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261013-advance-20261018-r06-decision-problem-foundations/#q-20261013-advance-20261018-r06-decision-problem-0025) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0016-08775 · q-20261013-advance-20261018-r06-decision-problem-0025 ## Original question and givens The explicit finite input set is Fin(6)={0,…,5} and its yes-instance set is [3, 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. 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 [3, 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. 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. - [mko-decision-problem](https://ocme.evemisslab.com/en/mko/mko-decision-problem/) ## Step-by-step derivation S001 · impliesBefore domain Fin(6);raw yes instances=[3, 4] After normalized yes set=[3, 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 dependenciesRule: finite_decision_spec_not_program_execution · Uses: G001 S002 · impliesBefore input=0;yes set=[3, 4] After specification value=No Conditions: none Use membership in the specification yes set for this cell,retaining every legal input. Step identifiers and dependenciesRule: finite_decision_complete_spec_cell · Uses: G001, S001 S003 · impliesBefore input=1;yes set=[3, 4] After specification value=No Conditions: none Use membership in the specification yes set for this cell,retaining every legal input. Step identifiers and dependenciesRule: finite_decision_complete_spec_cell · Uses: G001, S002 S004 · impliesBefore input=2;yes set=[3, 4] After specification value=No Conditions: none Use membership in the specification yes set for this cell,retaining every legal input. Step identifiers and dependenciesRule: finite_decision_complete_spec_cell · Uses: G001, S003 S005 · impliesBefore input=3;yes set=[3, 4] After specification value=Yes Conditions: none Use membership in the specification yes set for this cell,retaining every legal input. Step identifiers and dependenciesRule: finite_decision_complete_spec_cell · Uses: G001, S004 S006 · impliesBefore input=4;yes set=[3, 4] After specification value=Yes Conditions: none Use membership in the specification yes set for this cell,retaining every legal input. Step identifiers and dependenciesRule: finite_decision_complete_spec_cell · Uses: G001, S005 S007 · impliesBefore input=5;yes set=[3, 4] After specification value=No Conditions: none Use membership in the specification yes set for this cell,retaining every legal input. Step identifiers and dependenciesRule: 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, [3, 4], [[0, No], [1, No], [2, No], [3, Yes], [4, Yes], [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: 7c3d7554a1dd169c0b02060a6d502edbccee88b308bf99e9b66278cb68259d04 - candidate record SHA-256: 3f6bcaa1c5ba355c1f08acfe14e7ad3a5be56d294ccae15b78467e142bba42c5 - semantic review receipt SHA-256: 00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2 - question-first witness SHA-256: 198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1 - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261013-advance-20261018-r06-decision-problem-0025.json)