On Regular Message Sequence Chart Languages and Relationships to Mazurkiewicz Trace Theory

  • Rémi Morin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2030)

Abstract

Hierarchical Message Sequence Charts are a well-established formalism to specify telecommunication protocols. In this model, numerous undecidability results were obtained recently through algebraic approaches or relationships to Mazurkiewicz trace theory. We show how to check whether a rational language of MSCs requires only channels of finite capacity. In that case, we also provide an upper bound for the size of the channels. This enables us to prove our main result: one can decide whether the iteration of a given regular language of MSCs is regular if, and only if, the Star Problem in trace monoids (over some restricted independence alphabets) is decidable too.

References

  1. 1.
    Alur R. and Yannakakis M.: Model Checking of Message Sequence Charts. CONCUR’99, LNCS 1664 (1999) 114–129Google Scholar
  2. 2.
    Arnold A.: An extension of the notion of traces and asynchronous automata. Theoretical Informatics and Applications 25 (1991) 355–393Google Scholar
  3. 3.
    Ben-Abdallah H. and Leue S.: Syntactic Analysis of Message Sequence Chart Specifications. Technical report 96-12 (University of Waterloo, Canada, 1996)Google Scholar
  4. 4.
    Ben-Abdallah H. and Leue S.: Syntactic Detection of Process Divergence and Non-local Choice in Message Sequence Charts. TACAS’97, LNCS 1217 (1997) 259–274Google Scholar
  5. 5.
    Booch G., Jacobson I. and Rumbough J.: Unified Modelling Language User Guide. (Addison-Wesley, 1997)Google Scholar
  6. 6.
    Büchi J.R.: Weak second-order arithmetic and finite automata. Z. Math. Logik Grundlagen Math. 6 (1960) 66–92MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Caillaud B., Darondeau Ph., Hélouët L. and Lesventes G.: HMSCs as partial specifications... with PNs as completions. Proc. of MOVEP’2k, Nantes (2000) 87–103Google Scholar
  8. 8.
    Cori R., Métivier Y. and Zielonka W.: Asynchronous mappings and asynchronous cellular automata. Information and Computation 106 (1993) 159–202MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Diekert V. and Rozenberg G.: The Book of Traces. (World Scientific, 1995)Google Scholar
  10. 10.
    Droste M. and Kuske D.: Logical definability of recognizable and aperiodic languages in concurrency monoids. LNCS 1092 (1996) 233–251Google Scholar
  11. 11.
    Ebinger W. and Muscholl A.: Logical definability on infinite traces. Theoretical Comp. Science 154 (1996) 67–84MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Gastin P., Ochmański E., Petit A. and Rozoy, B.: On the decidability of the star problem. Information Processing Letters 44 (1992) 65–71MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Gunter E.L., Muscholl A. and Peled D.: Compositional Message Sequence Charts. TACAS 2001, LNCS (2001)-To appear.Google Scholar
  14. 14.
    Hélouët L., Jard C. and Caillaud B.: An effective equivalence for sets of scenarios represented by HMSCs. Technical report, PI-1205 (IRISA, Rennes, 1998)Google Scholar
  15. 15.
    Henriksen J.G, Mukund M., Narayan Kumar, K. and Thiagarajan P.S.: Towards a theory of regular MSC languages. Technical report (BRICS RS-99-52, 1999)Google Scholar
  16. 16.
    Henriksen J.G., Mukund M., Narayan Kumar K. and Thiagarajan P.S.: On message sequence graphs and finitely generated regular MSC language. LNCS 1853 (2000) 675–686Google Scholar
  17. 17.
    Henriksen J.G., Mukund M., Narayan Kumar K. and Thiagarajan P.S.: Regular collections of message sequence charts. MFCS 2000, LNCS 1893 (2000) 405–414Google Scholar
  18. 18.
    Holzmann G.J.: Early Fault Detection. TACAS’96, LNCS 1055 (1996) 1–13Google Scholar
  19. 19.
    Husson J.-Fr. and Morin R.: On Recognizable Stable Trace Languages. FoSSaCS 2000, LNCS 1784 (2000) 177–191Google Scholar
  20. 20.
    ITU-TS: Recommendation Z.120: Message Sequence Charts. (Geneva, 1996)Google Scholar
  21. 21.
    Kirsten D. and Richomme G.: Decidability Equivalence Between the Star Problem and the Finite Power Problem in Trace Monoids. Technical Report ISSN 1430-211X, TUD/FI99/03 (Dresden University of Technology, 1999)Google Scholar
  22. 22.
    Kuske D. and Morin R.: Pomsets for Local Trace Languages: Recognizability, Logic and Petri Nets. CONCUR 2000, LNCS 1877 (2000) 426–441CrossRefGoogle Scholar
  23. 23.
    Lamport L.: Time, Clocks and the Ordering of Events in a Distributed System. Comm. of the ACM, vol. 21, N 27 (1978)-ACMGoogle Scholar
  24. 24.
    Mazurkiewicz A.: Concurrent program schemes and their interpretations. Aarhus University Publication (DAIMI PB-78, 1977)Google Scholar
  25. 25.
    Mukund M., Narayan Kumar K. and Sohoni M.: Synthesizing distributed finite-state systems from MSCs. CONCUR 2000, LNCS 1877 (2000) 521–535CrossRefGoogle Scholar
  26. 26.
    Muscholl A., Peled D. and Su Z.: Deciding Properties for Message Sequence Charts. FoSSaCS’98, LNCS 1378 (1998) 226–242Google Scholar
  27. 27.
    Muscholl A.: Matching Specifications for Message Sequence Charts. FoSSaCS’99, LNCS 1578 (1999) 273–287Google Scholar
  28. 28.
    Muscholl A. and Peled D.: Message sequence graphs and decision problems on Mazurkiewicz traces. Proc. of MFCS’99, LNCS 1672 (1999) 81–91Google Scholar
  29. 29.
    Nielsen M., Plotkin G. and Winskel G.: Petri nets, events structures and domains, part 1. Relationships between Models of Concurrency, TCS 13 (1981) 85–108MATHMathSciNetGoogle Scholar
  30. 30.
    Nielsen M., Sassone V. and Winskel G.: Relationships between Models of Concurrency. Rex’93: A decade of concurrency, LNCS 803 (1994) 425–475Google Scholar
  31. 31.
    Ochmański E.: Regular behaviour of concurrent systems. Bulletin of the EATCS 27 (Oct. 1985) 56–67Google Scholar
  32. 32.
    Pratt V.: Modelling concurrency with partial orders. Int. J. of Parallel Programming 15 (1986) 33–71MATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Sakarovitch J.: The “last” decision problem for rational trace languages. Proc. LATIN’92, LNCS 583 (1992) 460–473Google Scholar
  34. 34.
    Thomas W.: On logical definability of trace languages. Technical University of Munich, report TUM-I9002 (1990) 172–182Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Rémi Morin
    • 1
  1. 1.Institut für AlgebraTechnische Universität DresdenDresdenGermany

Personalised recommendations