Minimal Union-Free Decompositions of Regular Languages

Authors:
Sergey Afonin;Denis Golomazov
Affiliations:
Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia;Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia
Venue:
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Year:
2009

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Abstract

A regular language is called union-free if it can be represented by a regular expression that does not contain the union operation. Every regular language can be represented as a finite union of union-free languages (the so-called union-free decomposition ), but such decomposition is not necessarily unique. We call the number of components in the minimal union-free decomposition of a regular language the union width of the regular language. In this paper we prove that the union width of any regular language can be effectively computed and we present an algorithm for constructing a corresponding decomposition. We also study some properties of union-free languages and introduce a new algorithm for checking whether a regular language is union-free.