Epsilon closure & automata

Question

I think I do not quite understand the concept of epsilon transitions when determining the language of a non-deterministic automata. For example in this automata:

The language is: 'A double sequence of a or a double sequence of b where there is a possibility of a baa sequence'.

But, the word a belongs to the automata too, doesn't it? (also the word b, and aaa and so on...)

Answer 1

An ε-transition is just a impromptu transition which doesn't consume any input.

When you are in a state which has outgoing ε-transitions it's like being in all of them until the automaton does something which is observable, from here the non determinism. The set of such states is the ε-closure of a state.

According to the layout you can have an arbitrary amount of baa prefixes followed by an arbitrary amount of of as or bs. So:

• empty
• baa
• baabaa
• a
• aa
• ba
• abab
• baabab
• ...