On Recognizable Stable Trace Languages

  • Jean-François Husson
  • Rémi Morin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1784)


We relate several models of concurrency introduced in the literature in order to extend classical Mazurkiewicz traces. These are mainly Droste’s concurrent automata and Arnold’s CCI sets of P-traces, studied in the framework of local trace languages. Also, a connection between these models and classical traces is presented in details through a natural notion of projection. These relationships enable us to use efficiently Arnold’s result in two other frameworks. First, we give a finite distributed implementation for regular CCI sets of P-traces (or, equivalently, finite stably concurrent automata) by means of bounded labelled Petri nets. Second, we present a new, simple and constructive method to relate Stark’s trace automata with Bednarczyk’s asynchronous transition systems. This improves a recent result in Scott domain theory.


  1. 1.
    Arnold A.: An extension of the notion of traces and asynchronous automata. Theoretical Informatics and Applications 25 (1991) 355–393MATHGoogle Scholar
  2. 2.
    Bednarczyk M.: Categories of asynchronous systems. PhD thesis (University of Sussex, 1987)Google Scholar
  3. 3.
    Bracho F., Droste M., Kuske D.: Representations of computations in concurrent automata by dependence orders. TCS 174 (1997) 67–96MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Diekert V., Rozenberg G.: The Book of Traces. (World Scientific, 1995)Google Scholar
  5. 5.
    Droste M.: Concurrency, automata and domains. LNCS 443 (1990) 195–208Google Scholar
  6. 6.
    Droste M., Shortt R.M.: From Petri nets to automata with concurrency. — Unpublished manuscript (1999) —Google Scholar
  7. 7.
    Ehrenfeucht A., Rozenberg G.: Partial (Set) 2-structures. Part II: State spaces of concurrent systems, Acta Informatica 27 (1990) 343–368MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Hoogers P.W., Kleijn H.C.M., Thiagarajan P.S.: A Trace Semantics for Petri Nets. Information and Computation 117 (1995) 98–114MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Husson J.-Fr.: Modélisation de la causalité par des relations d’indépendances. Thesis (Université Paul Sabatier de Toulouse, 1996)Google Scholar
  10. 10.
    Husson J.-Fr., Morin R.: Relationships between Arnold’s CCI sets of P-traces and Droste’s stably concurrent automata. Technical report MATH-AL-1-00 (Technische Universität Dresden, 2000)Google Scholar
  11. 11.
    Kleijn H.C.M., Morin R., Rozoy B.: A General Categorical Connection between Local Event Structures and Local Traces. FCT’99, LNCS 1684 (1999) 338349Google Scholar
  12. 12.
    Kuske D.: Nondeterministic automata with concurrency relations and domains. CAAP’94, LNCS 787 (1994) 202–217Google Scholar
  13. 13.
    Mazurkiewicz A.: Concurrent program schemes and their interpretations. Aarhus University Publication (DAIMI PB-78, 1977)Google Scholar
  14. 14.
    Morin R., Rozoy B.: On the Semantics of Place/Transition Nets. Concur’99, LNCS 1664 (1999) 447–462Google Scholar
  15. 15.
    Mukund M.: Petri Nets and Step Transition Systems. International Journal of Foundations of Computer Science 3 (1992) 443–478MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Nielsen M., Sassone V., Winskel G.: Relationships between Models of Concurrency. LNCS 803 (1994) 425–475Google Scholar
  17. 17.
    Schmitt V.: Stable trace automata vs. full trace automata. TCS 200 (1998) 45–100MATHCrossRefGoogle Scholar
  18. 18.
    Stark E.W.: Connections between concrete and abstract model of concurrent systems. LNCS 442 (1990) 53–79Google Scholar
  19. 19.
    Szpilrajn E.: Sur l’extension de l’ordre partiel. Fund. Math. 16 (1930) 386–389MATHGoogle Scholar
  20. 20.
    Winskel G.: Event structures. LNCS 255 (1987) 325–392Google Scholar
  21. 21.
    Zielonka W.: Notes on finite asynchronous automata. Theoretical Informatics and Applications 21 (1987) 99–135MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jean-François Husson
    • 1
  • Rémi Morin
    • 2
  1. 1.IRITUniversité Paul SabatierToulouseFrance
  2. 2.Institut für AlgebraTechnische Universität DresdenDresdenGermany

Personalised recommendations