NFA to DFA - GATECSE

'''Q:''' I know that $2^n$ are the maximum states in DFA for an $n$ state NFA. But what about the minimum no of states in a DFA for an $n$ state NFA?
'''Q:''' After converting from NFA to DFA and we get $2^n$ states. Now we apply minimization- how many states can we get after this?

Q: I know that $2^n$ are the maximum states in DFA for an $n$ state NFA. But what about the minimum no of states in a DFA for an $n$ state NFA?

A: I would say 1 because the $n$ states can be connected through $ε$ moves and hence all of these will be combines to a single start state in DFA.

Q: After converting from NFA to DFA and we get $2^n$ states. Now we apply minimization- how many states can we get after this?

In the worst case this can remain $2^n$ - that is no minimization can be possible. We can see this in the following example

NFA

DFA

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Q: I know that $2^n$ are the maximum states in DFA for an $n$ state NFA. But what about the minimum no of states in a DFA for an $n$ state NFA?

A: I would say 1 because the $n$ states can be connected through $ε$ moves and hence all of these will be combines to a single start state in DFA.

Q: After converting from NFA to DFA and we get $2^n$ states. Now we apply minimization- how many states can we get after this?

In the worst case this can remain $2^n$ - that is no minimization can be possible. We can see this in the following example

NFA

DFA