DFA to regular expression

Question

I have already read a couple soultions and tutorials, expecially on Stackoverflow, but can't help myself with a specific issue. To begin with, I have this DFA:

And could reduce it to this:

So that I have the regular expression at (aa|ba|cc)c but missing the returning d. Checking it that far with http://hackingoff.com/compilers/regular-expression-to-nfa-dfa it looks exactly like my starting DFA but without the d. I tried a lot but am very unsure how to write the d into the RE.

Answer 1

Your proposed sequence isn't quite correct, as pointed out by revo . The correct sequence is (aa|ba|c)c .

The regex version (in programming languages) of the whole DFA would be

/^(?:aa|ba|c)c(?:d(?:aa|ba|c)c)*$/

The formal regex would be

(aa|ba|c)c(d(aa|ba|c)c)*

(?:aa|ba|cc)c is the first sequence that you already figured out (everything from q0 to q6 , without the d path from q6 back to q0 ).

Once a d appears, you basically need the above sequence again . That second instance of the sequence including the d can be repeated any number of times, so you use the * quantifier.