An Algebra of Non-safe Petri Boxes

  • Raymond Devillers
  • Hanna Klaudel
  • Maciej Koutny
  • Franck Pommereau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2422)


We define an algebraic framework based on non-safe Petri nets, which allows one to express operations such as iteration, parallel composition, and transition synchronisation. This leads to an algebra of process expressions, whose constants and operators directly correspond to those used in Petri nets, and so we are able to associate nets to process expressions compositionally. The semantics of composite nets is then used to guide the definition of a structured operational semantics of process expressions. The main result is that an expression and the corresponding net generate isomorphic transition systems. We finally discuss a partial order semantics of the two algebras developed in this paper.


Petri nets process algebra operational semantics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    T. Basten and M. Voorhoeve: An Algebraic Semantics for Hierarchical P/T Nets. ICATPN’95, Springer, LNCS 935 (1995) 45–65.Google Scholar
  2. 2.
    E. Best and R. Devillers: Sequential and Concurrent Behaviour in Petri Net Theory. Theoretical Computer Science 55 (1988) 87–136.CrossRefMathSciNetGoogle Scholar
  3. 3.
    E. Best, R. Devillers and J. Hall: The Petri Box Calculus: a New Causal Algebra with Multilabel Communication. In: Advances in Petri Nets 1992, G. Rozenberg (Ed.). Springer, LNCS 609 (1992) 21–69.Google Scholar
  4. 4.
    E. Best, R. Devillers and M. Koutny: Petri Net Algebra. EATCS Monographs on TCS, Springer (2001).Google Scholar
  5. 5.
    G. Boudol and I. Castellani: Flow Models of Distributed Computations: Three Equivalent Semantics for CCS. Information and Computation 114 (1994) 247–314.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    P. Degano, R. De Nicola and U. Montanari: A Distributed Operational Semantics for CCS Based on C/E Systems. Acta Informatica 26 (1988) 59–91.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    R. Devillers, H. Klaudel, M. Koutny, E. Pelz and F. Pommereau: Operational Semantics for PBC with Asynchronous Communication. HPC’02, SCS (2002) 314–319.Google Scholar
  8. 8.
    R. Devillers, H. Klaudel, M. Koutny and F. Pommereau: Asynchronous Box Calculus. Technical Report CS-TR-759, Dept. of Comp. Sci., Univ. of Newcastle (2002).Google Scholar
  9. 9.
    J. Esparza, S. Römer and W. Vogler: An Improvement of McMillan’s Unfolding Algorithm. TACAS’96, Springer, LNCS 1055 (1996) 87–106.Google Scholar
  10. 10.
    R. J. van Glabbeek and F. V. Vaandrager: Petri Net Models for Algebraic Theories of Concurrency. PARLE’87, Springer, LNCS 259 (1987) 224–242.Google Scholar
  11. 11.
    U. Goltz and R. Loogen: A Non-interleaving Semantic Model for Nondeterministic Concurrent Processes. Fundamentae Informaticae 14 (1991) 39–73.zbMATHMathSciNetGoogle Scholar
  12. 12.
    R. Gorrieri and U. Montanari: On the Implementation of Concurrent Calculi in Net Calculi: two Case Studies. Theoretical Computer Science 141(1–2) (1995) 195–252.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    C. A. R. Hoare: Communicating Sequential Processes. Prentice Hall (1985).Google Scholar
  14. 14.
    P. W. Hoogers, H. C. M. Kleijn and P. S. Thiagarajan: An Event Structure Semantics for General Petri Nets. Theoretical Computer Science 153 (1996) 129–170.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    H. Klaudel and F. Pommereau: Asynchronous links in the PBC and M-nets. ASIAN’99, Springer, LNCS 1742 (1999) 190–200.Google Scholar
  16. 16.
    H. Klaudel and F. Pommereau: A concurrent and Compositional Petri Net Semantics of Preemption. IFM’2000, Springer, LNCS 1945 (2000) 318–337.Google Scholar
  17. 17.
    R. Milner: Communication and Concurrency. Prentice Hall (1989).Google Scholar
  18. 18.
    E. R. Olderog: Nets, Terms and Formulas. Cambridge Tracts in Theoretical Computer Science 23, Cambridge University Press (1991).Google Scholar
  19. 19.
    G. D. Plotkin: A Structural Approach to Operational Semantics. Technical Report FN-19, Computer Science Department, University of Aarhus (1981).Google Scholar
  20. 20.
    W. Reisig: Petri Nets. An Introduction. EATCS Monographs, Springer (1985).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Raymond Devillers
    • 1
  • Hanna Klaudel
    • 2
  • Maciej Koutny
    • 3
  • Franck Pommereau
    • 2
  1. 1.Département d’InformatiqueUniversité Libre de BruxellesBruxellesBelgium
  2. 2.LACLUniversité Paris 12CréteilFrance
  3. 3.Department of Computing ScienceUniversity of Newcastle upon TyneUK

Personalised recommendations