On the existence of prime decompositions

  • Authors:

  • Yo-Sub Han;Arto Salomaa;Kai Salomaa;Derick Wood;Sheng Yu

  • Affiliations:

  • System Technology Division, Korea Institute of Science and Technology, P.O. Box 131, Cheongryang, Seoul, Republic of Korea;Turku Centre for Computer Science, Joukahaisenkatu 35 B, 20520 Turku, Finland;School of Computing, Queens University, Kingston, Ontario K7L 3N6, Canada;Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong and Department of Computer Science, University of Western Ontario, London, Ontar ...;Department of Computer Science, University of Western Ontario, London, Ontario N6A 5B7, Canada

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

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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 it 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 non-regular unary languages that do not have prime decompositions. We also consider infinite factorizations of unary languages.