I am trying to understand how $\epsilon$ transitions work.
From what I've read, when you "go" to a state S that has arrows pointing outwards with $\epsilon$'s in it, you automatically go to those states too. That is, in the following diagram, when you are about to give the first digit as input to this FSA, you must consider you are not just in state S1 but in S1 AND S2.
Is this correct? Following this reasoning, when converting this NDFA to a DFA, one should have as first state S13.
The $\delta (S13, b) = S123$, as
- if I consider the path starting at S1, I will instantly go to S3
- if I consider the path starting at S3, as the input is b, this path dies
- if I consider the path starting at S1 with a b as input, I will get to S2.
I have a vague impression my understanding of $\epsilon$ transitions is wrong, as in some exercises I seem to get it done right, while in others wrong.