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Recognizable and rational languages of finite and infinite traces

  • Trace Theory
  • Conference paper
  • First Online:
STACS 91 (STACS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 480))

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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.

This work has been supported by the ESPRIT Basic Research Action No. 3166: Algebraic and Syntactic Methods in Computer Science (ASMICS) and by the PRC Math-Info.

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Authors and Affiliations

  1. Université Paris 6 LITP, 4, Place Jussieu, 75252, Paris Cedex 05, France

    Paul Gastin

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  1. Paul Gastin
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Christian Choffrut Matthias Jantzen

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© 1991 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/BFb0020790

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  • DOI: https://doi.org/10.1007/BFb0020790

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  • Print ISBN: 978-3-540-53709-0

  • Online ISBN: 978-3-540-47002-1

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