Converting a regular expression to a DFA

Question

I've been trying to convert the regular expression

to a non-deterministic finite automata (NFA) first using Thompson's construction, giving:

, which looks correct.

I am then using subset construction to create the DFA from the NFA, shown here.

But this does not look correct to me, as for example 0 followed by 0 is not valid according to the DFA I have constructed. I was wondering how should I be modelling the epsilon in the original regular expression, as I have simply treated it as a normal epsilon.

Answer 1

A single matches already - thus state B in your diagram for an dfa has to be already an accepting state (just mark it as accepting would not fix it!). I can't reconstruct your ideas, but you should end in something like

A --0--> (B)
A --1-->  C
B --0--> (B)
B --1-->  C
C --0--> (B)
C --1-->  C

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If you'll start to think from the other side, the regex (0|)(0|1)*0 could be simplified by removing the first part (0|) . This could be done because (0|1) matches everything that (0|) will match (and more). You can see it in your diagram for the nfa, too.

S0->S1->S2->S5 === S7->S7->S8->S11
S0->S3->S4->S5 === epsilon

Maybe this could help to get your thoughts in the right direction..