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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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References

  1. Arnold, A.: An extension of the notion of traces and asynchronous automata. RAIRO. Theoretical Informatics and Applications 25, 355–393 (1991) (Gauthiers-Villars)

    Google Scholar 

  2. Bollig, B., Leucker, M.: Message-passing automata are expressively equivalent to EMSO logic. Theoretical Computer Science 358, 150–172 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Büchi, J.R.: Weak second-order arithmetic and finite automata. Z. Math. Logik Grundlagen Math. 6, 66–92 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  4. Courcelle, B.: The monadic second-order logic of graphs X: Linear orderings. Theoretical Computer Science 160, 87–143 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Diekert, V., Métivier, Y.: Partial Commutation and Traces. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 457–534 (1997)

    Google Scholar 

  6. Dilworth, R.P.: A decomposition theorem for partially ordered sets. Ann. of Math. 51(2), 161–166 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  7. Doner, J.E.: Tree acceptors and some of their applications. J. Computer and Syst. Sciences 4, 406–451 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  8. Droste, M., Kuske, D.: Recognizable and logically definable languages of infinite computations in concurrent automata. International Journal of Foundations of Computer Science 9, 295–313 (1998)

    Article  MATH  Google Scholar 

  9. Droste, M., Gastin, P., Kuske, D.: Asynchronous cellular automata for pomsets. Theoretical Computer Science 247, 1–38 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ehrenfeucht, A., Rozenberg, G.: Partial (Set) 2-structures Part II: State spaces of concurrent systems. Acta Informatica 27, 343–368 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fanchon, J., Morin, R.: Regular sets of pomsets with autoconcurrency. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 402–417. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Gischer, J.L.: The equational theory of pomsets. Theoretical Computer Science 61, 199–224 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  13. Grabowski, J.: On partial languages. Fundamenta Informatica IV(2), 427–498 (1981)

    Google Scholar 

  14. Henriksen, J.G., Mukund, M., Narayan Kumar, K., Sohoni, M., Thiagarajan, P.S.: A Theory of Regular MSC Languages. Information and Computation 202, 1–38 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Hoogers, P.W., Kleijn, H.C.M., Thiagarajan, P.S.: A Trace Semantics for Petri Nets. Information and Computation 117, 98–114 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kiehn, A.: On the interrelationship between synchronised and non synchronised behaviour of Petri Nets. Journal of Information Processing and Cybernetics. EIK 24, 3–18 (1988)

    MathSciNet  MATH  Google Scholar 

  17. Kuske, D.: Asynchronous cellular automata and asynchronous automata for pomsets. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 517–532. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  18. Kuske, D.: Towards a language theory for infinite N-free pomsets. Theoretical Computer Science 299, 347–386 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kuske, D., Morin, R.: Pomsets for local trace languages. Journal of Automata, Languages and Combinatorics 7, 187–224 (2002)

    MathSciNet  MATH  Google Scholar 

  20. Lodaya, K., Weil, P.: Series-parallel languages and the bounded-width property. Theoretical Computer Science 237, 347–380 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  21. Morin, R.: Recognizable Sets of Message Sequence Charts. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 523–534. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  22. Mukund, M.: Petri Nets and Step Transition Systems. International Journal of Foundations of Computer Science 3, 443–478 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  23. Pratt, V.: Modelling concurrency with partial orders. International Journal of Parallel Programming 15, 33–71 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  24. Thatcher, W., Wright, J.B.: Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Systems Theory 2, 57–81 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  25. Thomas, W.: Languages, automata, and logic. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 389–455 (1997)

    Google Scholar 

  26. Vogler, W.: Modular Construction and Partial Order Semantics of Petri Nets. LNCS, vol. 625. Springer, Heidelberg (1992)

    MATH  Google Scholar 

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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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