Question 16233: A DFA Needs a Complete Total Deterministic Transition Table

Original question and givens

Use a complete deterministic finite automaton with states=Fin(3)={0,…,2}, alphabet=Fin(2)={0,…,1}, total row-state/column-symbol transition=[[1, 2], [0, 0], [0, 0]], unique start=1, and increasing accepting subset=[1]. Every transition output lies in this same state set. There are no epsilon transitions or nondeterministic branches. Read a finite word in symbol order; the empty word leaves the automaton at its start state. Give (state_count,alphabet_count,start,accepting,transition_cell_count,qualified?,complete_total_deterministic_table).

• G001 — Use a complete deterministic finite automaton with states=Fin(3)={0,…,2}, alphabet=Fin(2)={0,…,1}, total row-state/column-symbol transition=[[1, 2], [0, 0], [0, 0]], unique start=1, and increasing accepting subset=[1]. Every transition output lies in this same state set. There are no epsilon transitions or nondeterministic branches. Read a finite word in symbol order; the empty word leaves the automaton at its start state. Give (state_count,alphabet_count,start,accepting,transition_cell_count,qualified?,complete_total_deterministic_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-finite-automaton

Step-by-step derivation

DFA total state-symbol cell count := mul(3, 2)

DFA total state-symbol cell count = 6

same complete states Fin(3);alphabet Fin(2);row-state column-symbol table=[[1, 2], [0, 0], [0, 0]]

single original start=1;canonical accepting subset=[1];required transition cells=6

original transition cell state=0;symbol=0;complete original row=[1, 2]

single same-carrier next state=1

original transition cell state=0;symbol=1;complete original row=[1, 2]

single same-carrier next state=2

original transition cell state=1;symbol=0;complete original row=[0, 0]

single same-carrier next state=0

original transition cell state=1;symbol=1;complete original row=[0, 0]

single same-carrier next state=0

original transition cell state=2;symbol=0;complete original row=[0, 0]

single same-carrier next state=0

original transition cell state=2;symbol=1;complete original row=[0, 0]

single same-carrier next state=0

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 — Recompute DFA total state-symbol cell count with exact rational arithmetic, not rounded decimals.

Result

(3, 2, 1, [1], 6, Yes, complete_total_deterministic_table)

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.