Convert finite state machine to regular expression

Question

Is there a tool (or an algorithm) to convert a finite state machine into a regular expression?

(not the other way around, that would be easy).

Answer 1

I have implemented the state elimination algorithm for the http://www.brics.dk/automaton/ Java package. The implementation is based on the algorithm illustrated in Sipser, Michael. Introduction to the Theory of Computation. Vol. 2. Boston: Thomson Course Technology, 2006.

You can check it out at https://github.com/julianthome/autorex. Would be happy to get some feedback.