Deriving histories of nets with priority relation

  • Ryszard Janicki
  • Maciej Koutny
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 817)


Relational structures representing causality and weak causality can be used to provide a ‘truly concurrent’ semantics of Petri Nets with priorities. We show how to derive such structures by generalising the standard construction of causal partial orders based on occurrence nets.


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  1. 1.
    Best E., Devillers R.: Sequential and Concurrent Behaviour in Petri Net Theory. Theoretical Computer Science 55 (1987), 87–136.CrossRefGoogle Scholar
  2. 2.
    Best E., Koutny M.: Petri Net Semantics of Priority Systems. Theoretical Computer Science 94(1) (1992), 141–158.CrossRefGoogle Scholar
  3. 3.
    Chiola G., Donatelli S., Francheschinis G.: Priorities, Inhibitor Arcs and Concurrency in P/T Nets. Proc. of 12th Intern. Conf. on Appl. and Theory of Petri Nets, Gjern, Denmark (1991), 182–205.Google Scholar
  4. 4.
    Fräisse R.: Theory of Relations. North Holland (1986).Google Scholar
  5. 5.
    Gaifman H., Pratt V.: Partial Order Models of Concurrency and the Computation of Function. Proc. of Symposium on Logic in Computer Science (1987), 72–85.Google Scholar
  6. 6.
    Gerber R., Lee I.: A Resource-Based Bisimulation for Real-Time Systems. Information and Computation, to appear.Google Scholar
  7. 7.
    Hack M.: Petri Net Languages. Computation Structures Group Memo 127, MIT (1975).Google Scholar
  8. 8.
    Janicki R.: A Formal Semantics for Concurrent Systems with a Priority Relation. Acta Informatica 24 (1987), 33–55.CrossRefGoogle Scholar
  9. 9.
    Janicki R., Koutny M.: Invariant Semantics of Nets with Inhibitor Arcs. Proc. of CONCUR'91, Lecture Notes in Computer Science 527 (1991), 317–331.Google Scholar
  10. 10.
    Janicki R., Koutny M.: Invariants and Paradigms of Concurrency Theory. Proc. of PARLE'91, Lecture Notes in Computer Science 506 (1991), 59–74. Also appeared in Future Generation Computer Systems 8, 1992, pp. 423–435.Google Scholar
  11. 11.
    Janicki R., Koutny M.: Structure of Concurrency. Theoretical Computer Science 112 (1993), 5–52.CrossRefGoogle Scholar
  12. 12.
    Janicki R., Koutny M.: Order Structures and Generalisations of Szpilrajn's Theorem. Proc. of FST&TCS'93, Lecture Notes in Computer Science 761 (1993), 348–357.Google Scholar
  13. 13.
    Janicki R. and Lauer P.: Specification and Analysis of Concurrent Systems: The COSY Approach. Springer-Verlag, (1992).Google Scholar
  14. 14.
    Jorg W.B.: A subclass of Petri Nets as Design Abstraction for Parallel Architectures. ACM Computer Architecture News, Vol.18(4) (1990), 67–77.CrossRefGoogle Scholar
  15. 15.
    Lamport L.: What It Means for a Concurrent Program to Satisfy a Specification: Why No One has Specified Priority. 12th ACM Symposium on Principles of Programming Languages. New Orleans, Luisiana (1985), 78–83.Google Scholar
  16. 16.
    Nielsen M., Rozenberg G., Thiagarajan P.S.: Behavioural Notions for Elementary Net Systems. Distributed Computing 4 (1990), 45–57.CrossRefGoogle Scholar
  17. 17.
    Peterson J.L.: Petri Net Theory and the Modeling of Systems. Prentice Hall (1981).Google Scholar
  18. 18.
    Reisig W.: Petri Nets: An Introduction. Springer (1985).Google Scholar
  19. 19.
    Reisig W.: A Strong Part of Concurrency. In: G.Rozenberg (ed.), Advances in Petri Nets 1987, Lecture Notes in Computer Science 266, Springer (1987), 238–272.Google Scholar
  20. 20.
    Shields M.W.: On the Nonsequential Behaviour of Systems possessing a Generalised Free Choice Property. Technical Report, Computer Science Department, University of Edinburgh (1981).Google Scholar
  21. 21.
    Szpilrajn E.: Sur l'extension de l'ordre partiel. Fundamenta Mathematicae 16 (1930), 386–389.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Ryszard Janicki
    • 1
  • Maciej Koutny
    • 2
  1. 1.Department of Computer Science and SystemsMcMaster UniversityHamiltonCanada
  2. 2.Department of Computing ScienceUniversity of NewcastleNewcastle upon TyneUK

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