selfdoubt

Question

Give an example of DFA minimization where the initial state is final state and there are one or more final states

Answer 1

Any dfa which accepts epsilon will have initial state as final state.

Coming to the second part of your doubt: More than 1 final states and initial state as final state. So suppose

L= a language over {a,b}

L= atmost 2 a's={epsilon,a,aa,ab,ba,aba,.......}=b*+b*ab*+b*ab*ab*

So we have more than one final states here and initial state is also final.

So see the following dfa:

For further ref:https://www.cs.odu.edu/~toida/nerzic/390teched/regular/fa/min-fa.html

Comments

@ck

a simple example is generate the Minimized DFA for the Language L = {∈,ab}

Note that, when your language contain ∈, then your DFA should contain initial state as one of the final state.

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How to minimize a DFA with all states as the final states?

I have obtained DFA with all final states by performing the following steps

step 1.     epsilon NFA is converted into NFA --M1

step 2.     NFA obtained is converted into DFA --M2

M2 contains all final states now I am not understanding how do I minimize it?

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in M2 if all states are final states

=> it accepts every input including epsilon

=>the minimized dfa there will be only 1 state which is initial state as well as finite state.