Finding Regular expression for FSM with more than one final state
If we get more than one different regular expression for the same finite state machine with more than one final state, is it correct?


Rather than push the buttons mechanically, you have to understand what you're doing. Your task is to find a regular expression equivalent to a given FSM. This means that the language accepted by your regular expression has to be the same as the language accepted by the given FSM.

For every state $\sigma$ in the FSM, you can computer a regular expression $r_\sigma$ for the language $L_\sigma$ of all words upon reading of which the FSM ends up at the state $\sigma$ (this definition is valid in the deterministic case; for non-deterministic automata, it has to be slightly modified). The language $L$ accepted by the FSM consists of all words upon reading of which the FSM ends up at an accepting state. Given this data, you should be able to come up with a regular expression for $L$ using the regular expressions $r_\sigma$ for all accepting states &mdash; you just have to combine them in the correct way.