Prime decompositions of regular languages

Authors:
Yo-Sub Han;Kai Salomaa;Derick Wood
Affiliations:
System Technology Division, Korea Institute of Science and Technology, Seoul, Korea;School of Computing, Queen's University, Kingston, Ontario, Canada;Department of Computer Science, The Hong Kong University of Science and Technology, Kowloon, Hong Kong SAR
Venue:
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Year:
2006

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Abstract

We investigate factorizations of regular languages in terms of prime languages. A language is said to be strongly prime decomposable if any way of factorizing the language yields a prime decomposition in a finite number of steps. We give a characterization of the strongly prime decomposable regular languages and using the characterization we show that every regular language over a unary alphabet has a prime decomposition. We show that there exist co-context-free languages that do not have prime decompositions.