Use complete epsilon-NFA states=[s12, m12, f12, e112, e212, d12], alphabet=[a12, b12], start=s12, final_states=[f12], transitions=[[s12, null, m12], [s12, null, d12], [m12, a12, m12], [m12, b12, f12], [f12, null, e112], [e112, null, e212]]. Each transition is [from,input symbol or null,to], with null consuming no input. States/labels and transitions must qualify, and subsets are unique carrier subsets sorted lexicographically. Empty alphabet/final sets and empty subset states are allowed. Given subset S=[f12, m12]. Give (subset, NFA_final_states, intersection, accepting_subset, certificate).
G001 — Use complete epsilon-NFA states=[s12, m12, f12, e112, e212, d12], alphabet=[a12, b12], start=s12, final_states=[f12], transitions=[[s12, null, m12], [s12, null, d12], [m12, a12, m12], [m12, b12, f12], [f12, null, e112], [e112, null, e212]]. Each transition is [from,input symbol or null,to], with null consuming no input. States/labels and transitions must qualify, and subsets are unique carrier subsets sorted lexicographically. Empty alphabet/final sets and empty subset states are allowed. Given subset S=[f12, m12]. Give (subset, NFA_final_states, intersection, accepting_subset, 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 source snapshot while listing ordered fields without JavaScript.Radius uses its original mode to select6 or11 fields without padding;distinguish nonclaims from actual negations.
final set normalized UTF16=[f12];states nonempty,alphabet/finals/relation MAYEMPTY;DUPLICATE triples rejected in THIS model
Conditions: none
This model differs from the earlier NFA node:transition triples are unique and finals are sorted.Subsets must be actual carrier subsets;do not import old duplicate/final-order conventions.
EXACT ORIGINAL supplied S=[f12, m12];normalized SAME-machine final set=[f12]
After
actual intersection=[f12];accepting_subset=Yes;NO EPS closure inserted
Conditions: none
This is the definition of an accepting DFA subset,not NFA empty-word acceptance from an arbitrary unclosed S.The empty subset is a legal rejecting dead state.
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.