Recognizable and rational languages of finite and infinite traces

  • Paul Gastin
Trace Theory

DOI: 10.1007/BFb0020790

Part of the Lecture Notes in Computer Science book series (LNCS, volume 480)
Cite this paper as:
Gastin P. (1991) Recognizable and rational languages of finite and infinite traces. In: Choffrut C., Jantzen M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg

Abstract

Trace languages are used in computer science to provide a description of the behaviours of concurrent systems. If we are interested in systems which never stop then we have to consider languages of infinite traces. In this paper, we introduce and study recognizable and rational languages of finite and infinite traces. We characterize recognizable languages by means of a syntactic congruence. We prove that the family of recognizable languages is strictly included in the family of rational languages. Next, we study the closure properties of the family of recognizable languages. We prove that this family is closed under the Boolean operations and under concatenation. Contrary to the (finite) iteration, the infinite iteration of a finite trace is proved to be recognizable. We conclude this paper with some open problems.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Paul Gastin
    • 1
  1. 1.Université Paris 6 LITPParis Cedex 05France

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