Peter Linz Edition 4 Exercise 4.2 Question 14 (Page No. 114)

Question

Find an algorithm for determining whether a regular language $L$ contains an infinite number of even-length strings.

Answer 1

I think we can do this by:

1)- construct a dfa for the regular language L.

2)- now construct a dfa on sigma for even length strings L1.

3)- now, construct a dfa for (L intersection L1).

4)- if the transition graph of  dfa for (L intersection L1) contains a cycle in a path from initial to final vertex, then it means it contains an infinite number of even length strings.

Otherwise if it is not accepting anything, means L does not contain any even length strings.

Or if there is not any cycle in the transition graph, then it means it is accepting finite strings of even length.