Is it decidable whether the language accepted by a given FSA

Is it decidable whether the language accepted by a given FSA is infinite? Prove it.

Solution

Answer:

We have to reduce this to a graph problem. To decide on this , We need to see if there is a path from the start state to a final state that has a loop on it. Let us take the language L = { aaa , aabbb , ababb ...}

This language is set of strings that starts with \"a\" and ends with \"b\" . If we draw its DFA , we can encounter a loop in some state between start and final state. Thus we can say that language is infinite but decidable as accepted by tha DFA.