# Regular Expression describing language accepted by Finite State Automata

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

Mathematics Asked by AWu on November 12, 2021

Your regular expression is correct, though I, like rain1, would simplify it to $$(01mid 10)^*$$: if you let $$u=01$$ and $$v=10$$, the automaton accepts any string over the alphabet $${u,v}$$.

Answered by Brian M. Scott on November 12, 2021

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