The Box Algebra —; A Model of Nets and Process Expressions

  • Eike Best
  • Raymond Devillers
  • Maciej Koutny
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1639)


The paper outlines a Petri net as well as a structural operational semantics for an algebra of process expressions. It specifically addresses this problem for the box algebra, a model of concurrent computation which combines Petri nets and standard process algebras. The paper proceeds in arguably the most general setting. For it allows infinite operators, and recursive definitions which can be unguarded and involve infinitely many recursion variables. The main result is that it is possible to obtain a framework where process expressions can be given two, entirely consistent, kinds of semantics, one based on Petri nets, the other on SOS rules.


Net-based algebraic calculi relationships between net theory and other approaches process algebras box algebra refinement recursion SOS semantics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Baeten, W.P. Weijland: Process Algebra. Cambridge Tracts in Theoretical Computer Science 18 (1990).Google Scholar
  2. 2.
    E. Best, R. Devillers: Sequential and Concurrent Behaviour in Petri Net Theory. Theoretical Computer Science 55:87–136 (1988).CrossRefMathSciNetGoogle Scholar
  3. 3.
    E. Best, R. Devillers, J. Esparza: General Refinement and Recursion Operators for the Petri Box Calculus. Springer-Verlag, LNCS 665:130–140 (1993).Google Scholar
  4. 4.
    E. Best, R. Devillers, J.G. Hall: The Petri Box Calculus: A New Causal Algebra with Multilabel Communication. Springer-Verlag, LNCS 609:21–69 (1992.Google Scholar
  5. 5.
    E. Best, R. Devillers, M. Koutny: Petri Nets, Process Algebras and Concurrent Programming Languages. Lectures on Petri Nets II: Applications, Advances in Petri Nets. Springer-Verlag, LNCS 1492:1–84 (1998).Google Scholar
  6. 6.
    E. Best, R. Devillers, M. Koutny: Petri Net Algebra. Book Manuscript (1999).Google Scholar
  7. 7.
    G. Boudol, I. Castellani: Flow Models of Distributed Computations: Event Structures and Nets. Rapport de Recherche, INRIA, Sophia Antipolis (1991).Google Scholar
  8. 8.
    P. Degano, R. De Nicola, U. Montanari: A Distributed Operational Semantics for CCS Based on C/E Systems. Acta Informtaica 26:59–91 (1988).CrossRefzbMATHGoogle Scholar
  9. 9.
    R. Devillers: S-invariant Analysis of Recursive Petri Boxes. Acta Informatica 32:313–345 (1995).zbMATHMathSciNetGoogle Scholar
  10. 10.
    R. Devillers, M. Koutny: Recursive Nets in the Box Algebra. Proc. of CSD’ 98 Conference, Fukushima, Japan, IEEE CS, 239–249 (1998).Google Scholar
  11. 11.
    U. Goltz: On Representing CCS Programs by Finite Petri Nets. Springher-Verlag, LNCS 324:339–350 (1988).Google Scholar
  12. 12.
    U. Goltz, R. Loogen: A Non-interleaving Semantic Model for Nondeterministic Concurrent Processes. Fundamenta Informaticae 14:39–73 (1991).zbMATHMathSciNetGoogle Scholar
  13. 13.
    M. Hesketh, M. Koutny: An Axiomatisation of Duplication Equivalence in Petri Box Calculus. Springer-Verlag, LNCS 1420:165–184 (1998).Google Scholar
  14. 14.
    C.A.R. Hoarae: Communicating Sequential Processes. Prentice Hall (1985).Google Scholar
  15. 15.
    R. Janicki, P.E. Lauer: Specification and Analysis of Concurrent Systems —; the COSY Approach. Springer-Verlag, LNCS EATCS Monographs on Theoretical Computer Science (1992).Google Scholar
  16. 16.
    M. Koutny, E. Best: Fundamental Study: Operational and Denotational Semantics for the Box Algebra. Theoretical Computer Science 211:1–83 (1999).zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    A. Mazurkiewicz: Trace Theory. Springer-Verlag, LNCS 255:279–324 (1987).Google Scholar
  18. 18.
    R. Milner: Communication and Currency. Prentice hall (1989).Google Scholar
  19. 19.
    T. Murata: Petri Nets: Properties, Analysis and Applications. Proc. IEEE 77:541–580(1989).CrossRefGoogle Scholar
  20. 20.
    E.-R. Olderog: Nets, Terms and Formulas. Cambridge Tracts in Th. Comp. Sci. 23 (1991).Google Scholar
  21. 21.
    G. Plotkin: A Structural Approach to Operational Semantics. DAIMI Technical Report FN-19, Computer Science Department, University of Arhus (1981).Google Scholar
  22. 22.
    W. Reisig: Petri Nets. An introduction. Springer-Verlag, EATCS Monographs on Theoretical Computer Science (1985).Google Scholar
  23. 23.
    D. Taubner: Finite Representation of CCS and TCSP Programs by Automata and Petri Nets. Springer-Verlag, LNCS 369 (1989).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Eike Best
    • 1
  • Raymond Devillers
    • 2
  • Maciej Koutny
    • 3
  1. 1.Fachb. Inf.Carl von Ossietzky UniversitätOldenburgGermany
  2. 2.Départ. d’Inform.Université Libre de BruxellesBruxellesBelgium
  3. 3.Dept. of Comp. Sci.University of NewcastleNewcastle upon TyneUK

Personalised recommendations