Hopefully I am including the image correctly or this won't make any sense. I am trying to figure out a regular expression for what this FSA accepts. From what I can tell it accepts any combination of 01 or 10 repeated. Wouldn't the expression then be ((01)* | (10)*) *
I believe I have what it should be as correct I just don't know if I am representing that answer as a regular expression in the correct form. Any help would be appreciated
Your regular expression is correct, though I, like rain1, would simplify it to $(01\mid 10)^*$: if you let $u=01$ and $v=10$, the automaton accepts any string over the alphabet $\{u,v\}$.