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Strong bisimilarity on nets: A new concept for comparing net semantics

  • Ernst-Rüdiger Olderog
Technical Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 354)

Abstract

We extend Park's notion of strong bisimilarity from automata to safe Petri nets. The underlying strong bisimulation is a relation on places which when lifted to the reachable markings preserves their token game and distribution over the places. As a consequence, strongly bisimilar nets have exactly the same concurrent computations as formalised by their causal nets.

We apply this concept of strong bisimilarity to the analysis of a previously defined operational Petri net semantics for process terms with operators from CCS. CSP and COSY. We show that the resulting Petri nets are strongly bisimilar to those obtained by the standard compositional net semantics. Hence the operational net semantics represents all the concurrency that is intended by the compositional net semantics. On the other hand, the operational net semantics yields more often finite nets than the compositional one.

Key words

Strong bisimilarity labelled place/transitions nets safeness causal nets process terms CCS CSP COSY operational and compositional net semantics 

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References

  1. [Be 87]
    E. Best, COSY: its relation to nets and CSP, in: W. Brauer, W. Reisig, G. Rozenberg (Eds.), Petri Nets: Applications and Relationships to Other Models of Concurrency, Lecture Notes in Comput. Sci. 255 (Springer-Verlag, 1987) 416–440.Google Scholar
  2. [BHR 84]
    S.D. Brookes, C.A.R. Hoare, A.W. Roscoe, A theory of communicating sequential processes, J. ACM 31 (1984) 560–599.CrossRefGoogle Scholar
  3. [By 86]
    M. Broy, Process semantics of communicating concurrent processes, Bericht MIP-8602, Fak. Math. u. Inform., Univ. Passau,1986.Google Scholar
  4. [DDM 87a]
    P. Degano, R. DeNicola, U. Montanari, CCS is an (augmented) contact-free C/E system, in: M. Venturini Zilli (Ed.), Math. Models for the Semantics of Parallelism, Lecture Notes in Comput. Sci. 280 (Springer-Verlag, 1987) 144–165.Google Scholar
  5. [DDM 87b]
    P. Degano, R. DeNicola, U. Montanari, A distributed operational semantics for CCS based on condition/event systems, Nota Interna B4-21, Dept. Comput. Sci., Univ. of Pisa, 1987 (to appear in Acta Inform.).Google Scholar
  6. [DDM 88]
    P. Degano, R. DeNicola, U. Montanari, On the consistency of "truly concurrent" operational and denotational semantics, in: Proc. Logics in Computer Science '88, Edinburgh, 1988.Google Scholar
  7. [DM 87]
    P. Degano, U. Montanari, Concurrent histories: a basis for observing distributed systems, J. Comput. Syt. Sci. 34 (1987) 442–461.Google Scholar
  8. [GV 87]
    R.J. van Glabbeek, F.W. Vaandrager, Petri net models for algebraic theories of concurrency, in: J.W. de Bakker; A.J. Nijman, P.C. Treleaven (Eds.), Proc. PARLE Conf., Eindhoven, Vol. II, Lecture Notes in Comput. Sci. 259 (Springer-Verlag, 1987) 224–242.Google Scholar
  9. [GM 84]
    U. Goltz, A. Mycroft, On the relationship of CCS and Petri nets, in: J. Paredaens (Ed.), Proc. 11th Coll. Automata, Languages and Programming, Lecture Notes in Comput. Sci. 172 (Springer-Verlag, 1984) 196–208.Google Scholar
  10. [Go 88a]
    U. Goltz, Über die Darstellung von CCS-Programmen durch Petrinetze, Doctoral Diss., RWTH Aachen, 1988.Google Scholar
  11. [Go 88b]
    U. Goltz, On representing CCS programs by finite Petri nets, Arbeitspapiere der GMD 290, Gesellschaft Math. Datenverarb., St. Augustin, 1988.Google Scholar
  12. [Ho 85]
    C.A.R. Hoare, Communicating Sequential Processes (Prentice-Hall, London, 1985).Google Scholar
  13. [LTS 79]
    P.E. Lauer, P.R. Torrigiani, M.W. Shields, COSY — A system specification language based on paths and processes, Acta Inform. 12 (1979) 109–158.CrossRefGoogle Scholar
  14. [Mi 80]
    R. Milner, A Calculus of Communicating Systems, Lecture Notes in Comput. Sci. 92 (Springer-Verlag, 1980).Google Scholar
  15. [Ol 87]
    E.-R. Olderog, Operational Petri net semantics for CCSP, in: G. Rozenberg (Ed.), Advances in Petri Nets 1987, Lecture Notes in Comput. Sci. 266 (Springer-Verlag, 1987) 196–223.Google Scholar
  16. [Ol 89]
    E.-R. Olderog, Nets, terms and formulas: three views of concurrent processes and their relationship (to apear 1989).Google Scholar
  17. [OH 86]
    E.-R. Olderog, C.A.R. Hoare, Specification-oriented semantics for communicating processes, Acta Inform. 23 (1986) 9–66.Google Scholar
  18. [Pa 81]
    D. Park, Concurrency and automata on infinite sequences, in: P. Deussen (Ed.), Proc. 5th GI Conf. on Theoret. Comput. Sci., Lecture Notes in Comput. Sci. 104 (Springer-Verlag, 1981).Google Scholar
  19. [Pe 77]
    C.A. Petri, Non-sequential processes, Internal Report GMD-ISF-77-5 Gesellschaft Math. Datenverarb., St. Augustin, 1977.Google Scholar
  20. [Pl 81]
    G.D. Plotkin, Structured approach to operational semantics, Tech. Report DAIMI FN-19, Comput. Sci. Dept., Aarhus Univ., 1981.Google Scholar
  21. [Pl 82]
    G.D. Plotkin, An operational semantics for CSP, in: D. Bjorner (Ed.), Formal Description of Programming Concepts II (North-Holland, Amsterdam, 1982) 199–225.Google Scholar
  22. [Po 85]
    L. Pomello, Some equivalence notions for concurrent systems — an overview, in: G. Rozenberg (Ed.), Advances in Petri Nets 1985, Lecture Notes in Comput. Sci. 222 (Springer-Verlag, 185) 381–400.Google Scholar
  23. [Re 85]
    W. Reisig, Petri Nets, An Introduction, EATCS Monographs on Theoret. Comput. Sci. (Springer-Verlag, 1985).Google Scholar
  24. [Ta 87]
    D. Taubner, Theoretical CSP and formal languages, Bericht TUM-I8706, Inst. f. Inform., TU München, 1987.Google Scholar
  25. [Wi 82]
    G. Winskel, Event structure semantics of CCS and related languages, in: E.M. Schmidt (Ed.), Proc. 9th Coll. Automata, Languages and Programming, Lecture Notes in Comput. Sci. 140 (Springer-Verlag, 1982).Google Scholar
  26. [Wi 84]
    G. Winskel, A new definition of morphism on Petri nets, in: M. Fontet, K. Mehlhorn (Eds.), Proc. 1st Symp. Theoret. Aspects of Comput. Sci., Lecture Notes in Comput. Sci. 166 (Springer-Verlag, 1984) 140–150.Google Scholar
  27. [Wi 87]
    G. Winskel, Event structures, in: W. Brauer, W. Reisig, G. Rozenberg (Eds.), Petri Nets: Application and Relationship to Other Models of Concurrency, Lecture Notes in Comput. Sci. 255 (Springer-Verlag, 1987) 325–392.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Ernst-Rüdiger Olderog
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität KielKiel 1Fed. Rep. Germany

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