Conversion of FA to Regular Expression If there is a transition with no input in the FA, when it is converted to a regular expression should it be accepted as ɛ transition? As an example picture shown below, should regular expression showing possible transitions between 1 and 3 (1-2-3 , 1-3) be accepted (ab+ɛ) or just ab?
The regular expression is supposed to match (exactly) all of the words that the automaton accepts. If you pretend that some of the transitions of the automaton don't exist, you're effectively converting a different automaton, and that automaton probably accepts different strings from the ones you're supposed to accept.

In this specific case, pretending that there's no $\varepsilon$-transition from the first state to the third one means that the automaton no longer accepts the word&nbsp;$c$.