Minimization of dfa

Question

Question 6.

Comments

In DFAs, the path taken in the automaton are deterministic and reach one specific state, so all the strings in the language reach one accepted state and all the other strings on this alphabet reach non-accepting states. 

On switching the final states with non-final states we are saying accept every string that doesn't reach an accepting state in the original automaton, don't accept any string that reach an accepting state in the original automaton. Simply means strings not in language L of original DFA.

Note: 

1)There can be one or more final states in an automaton but all the strings that are in the language L reach one final state which can be any of the final states. 

2) Switching of final and non final states is valid ONLY for DFA and not for NFA. To find complement of NFA, convert NFA -> DFA then switch final <-> Non final states.

Answer 1

we can take an example . both L and complement of L . both are minimal

Answer 2

From a minimal DFA, when you interchange final and non-final states, the language also gets complemented, which is not applicable for an NFA.