# Constructing finite state automata corresponding to regular expressions. Are my solutions correct?

I have drawn my answers in paint, are they correct?

(4c) For the alphabet {0, 1} construct ﬁnite state automata corresponding to each of the following regular expressions:

(i) 0

(ii) 1 | 0

(iii) 0 * (1 | 0)

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Your 4ciii solution can be much simpler. Hint -- construct an automaton for $0^*$. Then think how to convert that into an automaton for $0^*(1|0)$, realizing there are two cases to that, and you can apparently use $\epsilon$ moves. –  David Lewis Apr 26 '12 at 7:23

iii As David Lewis commented, this is much more complicated than necessary. Look at each of your $\epsilon$-transitions and consider whether it is really achieving anything. Some of them do have a purpose, but most of them don't. The tidiest automaton for this language doesn't have any $\epsilon$-transitions. Your automaton does recognise the right language, though.