Conference paper

Publication year: 2015

Pages: 1009-1040

Journal: International Journal of Foundations of Computer Science

Volume number: 26

Issue number: 8

ISSN: 0129-0541

eISSN: 1793-6373

Open access status: Green

DOI Link: https://doi.org/10.1142/S0129054115400110

Conference: 14th International Conference on Automata and Formal Languages (AFL)

Publisher: World Scientific Publishing

Abstract: 
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. As an interesting special case also one-unambiguous regular expressions, a sort of a deterministic version of a regular expression, are considered. We also briefly recall the known bounds for the removal of spontaneous transitions (epsilon-transitions) on non-epsilon-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 new developments on the state elimination algorithm that converts finite automata to regular expressions.

Harvard Citation style: Gruber, H. and Holzer, M. (2015) From Finite Automata to Regular Expressions and Back - A Summary on Descriptional Complexity, International Journal of Foundations of Computer Science, 26(8), pp. 1009-1040. https://doi.org/10.1142/S0129054115400110

APA Citation style: Gruber, H., & Holzer, M. (2015). From Finite Automata to Regular Expressions and Back - A Summary on Descriptional Complexity. International Journal of Foundations of Computer Science. 26(8), 1009-1040. https://doi.org/10.1142/S0129054115400110