# prove/disprove if L(B) = (̅L̅(̅A̅)̅)̅, then NFA A is actually a DFA.

im stuck in a homework question in Automata theory: Given an NFA A over finite Alphabet, let B be NFA with complement Accept states (e.g every accept state in A is not an accept state in B and vice versa)

prove/disprove if L(B) = (̅L̅(̅A̅)̅)̅ (complement of language), then NFA A is actually a DFA.

i tried many examples of NFA but couldn't find one that satisfies the initial assumption that L(B) = complement of L(A).

thanks for the help!

• I'm having trouble understanding your notation. In the title of your question, do you mean to complement the whole language $L(A)$, or are you complementing pieces of it? – ShyPerson Jun 19 at 4:31