Use complete epsilon-NFA states=[s10, m10, f10, e110, e210, d10], alphabet=[a10, b10], start=s10, final_states=[f10], transitions=[[s10, null, m10], [s10, null, d10], [m10, a10, m10], [m10, b10, f10], [f10, null, e110], [e110, null, e210]]. 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=[f10, m10]. Give (subset, NFA_final_states, intersection, accepting_subset, certificate).
G001 — Use complete epsilon-NFA states=[s10, m10, f10, e110, e210, d10], alphabet=[a10, b10], start=s10, final_states=[f10], transitions=[[s10, null, m10], [s10, null, d10], [m10, a10, m10], [m10, b10, f10], [f10, null, e110], [e110, null, e210]]. 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=[f10, m10]. 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=[f10];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=[f10, m10];normalized SAME-machine final set=[f10]
After
actual intersection=[f10];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.