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

Hermann Gruber, Markus Holzer
2015 International Journal of Foundations of Computer Science  
The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present 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 (ε-transitions) on non-ε-free nondeterministic devices. Moreover, we report on
more » ... 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.
doi:10.1142/s0129054115400110 fatcat:glifsfoc4jgw7cpuyxjwlwcq6a