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Pomset Languages of Finite Step Transition Systems

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Applications and Theory of Petri Nets (PETRI NETS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5606))

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Abstract

Step transition systems form a powerful model to describe the concurrent behaviors of distributed or parallel systems. They offer also a general framework for the study of marking graphs of Petri nets [22]. In this paper we investigate a natural labeled partial order semantics for step transition systems. As opposed to [19] we allow for autoconcurrency by considering steps that are multisets of actions. First we prove that the languages of step transition systems are precisely the width-bounded languages that are step-closed and quasi-consistent. Extending results from [19] we focus next on finite step transition systems and characterize their languages in the line of Buchi’s theorem. Our main result present six equivalent conditions in terms of regularity and MSO-definability for a set of labeled partial orders to be recognized by some finite step transition system.

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Author information

Authors and Affiliations

  1. CNRS, LAAS, 7 avenue du colonel Roche, F-31077, Toulouse, France

    Jean Fanchon

  2. Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, F-31077, Toulouse, France

    Jean Fanchon

  3. Laboratoire d’Informatique Fondamentale de Marseille, LIF, CNRS, UMR 6166, France

    Rémi Morin

  4. Aix-Marseille Université, 163, avenue de Luminy, Case 901, F-13288, Marseille, France

    Rémi Morin

Authors
  1. Jean Fanchon
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  2. Rémi Morin
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università del Piemonte Orientale, via Bellini 25/G, 15100, Alessandria, Italy

    Giuliana Franceschinis

  2. Institut für Informatik, Universität Rostock, Schwaansche Str. 2, 18051, Rostock, Germany

    Karsten Wolf

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Fanchon, J., Morin, R. (2009). Pomset Languages of Finite Step Transition Systems. In: Franceschinis, G., Wolf, K. (eds) Applications and Theory of Petri Nets. PETRI NETS 2009. Lecture Notes in Computer Science, vol 5606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02424-5_7

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  • DOI: https://doi.org/10.1007/978-3-642-02424-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02423-8

  • Online ISBN: 978-3-642-02424-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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