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Recognizing a language given an automaton

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I'm trying to figure out which language can be recognized in this automaton

Automata http://cdn.imghack.se/images/64b81d259a1d403b810dd9744dc222f7.jpg

According to Wikipedia here "The language L ⊆ Σ* recognized by an automaton is the set of all the words that are accepted by the automaton."

So using what Wikipedia states and knowing that this automaton is a finite state automaton, I would dare to say that this automaton accepts regular languages.

If I would use M to define this automaton then I could say:

The language recognized by M is the regular language given by a certain regular expression.

But I'm having a a hard time figuring out the regular expression.

I'm not sure of about this but here is what I think the regular expression looks like

$$ L = (a|b)(a|b)^*a^* $$

I would appreciate any help in this matter


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