Im having trouble figuring out how to determine if two finite automata are the same apart from renumbered states.
More specifically, heres an example:
It's easy to generate a regular expression by hand and see that both FA produce: b + (ab*a(a+b)), though their states are renumbered, they are identical.
What I'm trying to do is figure out a way to check if the two states are the same apart from state renumbering without generating a regular expression.
Since the states are just renumbered, I'm thinking it has something to do with permutations of the states(1 2 3 4) but am not seeing how to determine if they are equivalent. I'm thinking it has something to do with input like this and relating it to the 24 permutations of the states:
Left Right 1 a 2 4 a 3 1 b 4 4 b 1 2 a 3 3 a 2 2 b 2 3 b 3 3 a 4 2 a 1 3 b 4 2 b 1
Im more so trying to figure out the algorithm to renumber the states Any ideas or help is greatly appreciated!