Use the complete finite grammar: nonterminals=[S2, A2], terminals=[a2, b2], start=S2, productions=[[S2, [a2, A2]], [A2, [b2, A2]], [A2, []]] and allow_epsilon=true. Alphabets must be unique and disjoint, the start belongs to nonterminals, and each production [lhs,rhs] has exactly one nonterminal lhs and a finite legal-symbol rhs. Empty rhs is permitted only under the explicit epsilon convention. Keep original symbol and production order. Give (nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate).
G001 — Use the complete finite grammar: nonterminals=[S2, A2], terminals=[a2, b2], start=S2, productions=[[S2, [a2, A2]], [A2, [b2, A2]], [A2, []]] and allow_epsilon=true. Alphabets must be unique and disjoint, the start belongs to nonterminals, and each production [lhs,rhs] has exactly one nonterminal lhs and a finite legal-symbol rhs. Empty rhs is permitted only under the explicit epsilon convention. Keep original symbol and production order. Give (nonterminals, terminals, start, productions, allow_epsilon, grammar_qualified, certificate).
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.
Keep the original historical interface marker while listing ordered source fields without JavaScript.Tags are not additional evidence;fixed No markers retain their source claim scope.
ORIGINAL production index=0;lhs=S2,rhs=[a2, A2];N=[S2, A2],T=[a2, b2],allow_epsilon=Yes
After
lhs is ONE declared nonterminal;every rhs symbol legal;empty rhs accepted ONLY under the explicit epsilon convention;original production position retained
Conditions: none
Each production has one nonterminal on the left.Check every right-hand symbol and the explicit epsilon convention.Duplicate production positions may exist;sorting them would change first-witness indices.
ORIGINAL production index=1;lhs=A2,rhs=[b2, A2];N=[S2, A2],T=[a2, b2],allow_epsilon=Yes
After
lhs is ONE declared nonterminal;every rhs symbol legal;empty rhs accepted ONLY under the explicit epsilon convention;original production position retained
Conditions: none
Each production has one nonterminal on the left.Check every right-hand symbol and the explicit epsilon convention.Duplicate production positions may exist;sorting them would change first-witness indices.
ORIGINAL production index=2;lhs=A2,rhs=[];N=[S2, A2],T=[a2, b2],allow_epsilon=Yes
After
lhs is ONE declared nonterminal;every rhs symbol legal;empty rhs accepted ONLY under the explicit epsilon convention;original production position retained
Conditions: none
Each production has one nonterminal on the left.Check every right-hand symbol and the explicit epsilon convention.Duplicate production positions may exist;sorting them would change first-witness indices.
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.