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The equivalence of finite automata and regular expressions d ates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the pr esent paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. We also briefly recall the known bounds for the removal of spontaneous transitions (e-transitions) on non-e-free nondeterministic devices. Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination algorithm that converts finite automata to regular expressions.

From Finite Automata to Regular Expressions and Back — A Summary on Descriptional Complexity