Skip to main content
SpringerLink
Log in

The box calculus: A new causal algebra with multi-label communication

  • Conference paper
  • First Online:
Advances in Petri Nets 1992

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 609))

Abstract

A new Petri net calculus called the calculus of Petri Boxes is described. It has been designed to allow reasoning about the structure of a net and about the relationship between nets, and to facilitate the compositional semantic translation of high level constructs such as blocks, variables and atomic actions into elementary Petri nets. The calculus is located ‘midway’ in such a translation.

This paper first defines an algebra of Box expressions. A corresponding algebra of Boxes is then defined and used compositionally as a semantic model of Box expressions. The two algebras feature a general asynchronous communication operation extending that of CCS. Synchronisation is defined as a unary operator. The algebras also include refinement, iteration and recursion. It is shown how they can be used to describe data and blocks.

As the main results of this paper, it is proved that the Box algebra satisfies various desirable structural laws and enjoys two important behavioural properties. The paper also contains an example proof of a mutual exclusion protocol.

Work done within the Esprit Basic Research Action 3148 D→e→M→O→N (Design Methods Based on Nets).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.C.M.Baeten and W.P.Weijland: Process Algebra. Cambridge Tracts in Theoretical Computer Science (1990).

    Google Scholar 

  2. J.W.de Bakker and J. Zucker: Processes and the Denotational Semantics of Concurrency. Information and Control 54, 70–120 (1984).

    Google Scholar 

  3. E.Best: Relational Semantics of Concurrent Programs (with some Applications). Formal Description of Programming Concepts II (ed. D.BjØrner), North Holland, pp.431–452 (1982).

    Google Scholar 

  4. E. Best: Concurrent Behaviour: Sequences, Processes and Axioms. Seminar on Concurrency, Carnegie-Mellon University, Pittsburgh, PA, July 9–11, 1984 (eds. S.D.Brookes; A.W.Roscoe; G.Winskel) Springer-Verlag Lecture Notes in Computer Science Vol. 197, 221–245 (1985).

    Google Scholar 

  5. E. Best: COSY and its Relationship to CSP. Second Advanced Course on Petri Nets, Bad Honnef, Springer-Verlag Lecture Notes in Computer Science Vol. 255, 416–440 (1986).

    Google Scholar 

  6. E. Best: Weighted Basic Petri Nets. Concurrency'88, Springer-Verlag Lecture Notes in Computer Science Vol. 335, 257–276 (1988).

    Google Scholar 

  7. E.Best: Kausale Semantik nichtsequentieller Programme. (In German.) R.Oldenbourg-Verlag, GMD-Bericht Nr.174 (1989).

    Google Scholar 

  8. E.Best, L.Cherkasova and H.G.Linde: Compositional Process Semantics of the Box Algebra. To appear.

    Google Scholar 

  9. E. Best and R. Devillers: Sequential and Concurrent Behaviour in Petri Net Theory. Theoretical Computer Science Vol. 55, 87–136 (1987).

    Google Scholar 

  10. E.Best, R.Devillers, A.Kiehn and L.Pomello: Fully Concurrent Bisimulation. Technical Report LIT-202, Univ. Bruxelles (July 1989). Appeared in Acta Informatica Vol.28 with the changed title: Concurrent Bisimulation in Petri Nets, 231–264 (1991).

    Google Scholar 

  11. E.Best, R.Devillers and J.Hall: The Box Calculus: a New Causal Algebra with Multi-label Communication. Technical Report, Computing Laboratory, University of Newcastle-upon-Tyne (1992).

    Google Scholar 

  12. E.Best and R.P.Hopkins: A Basic Petri Net Programming Notation. To appear.

    Google Scholar 

  13. E.Best (ed.): Technical Annex of the Esprit Basic Research Action No. 3148 DEMON. GMD-Arbeitsbericht Nr.435 (1990).

    Google Scholar 

  14. E.Best, R.Devillers and J.Esparza: General Refinement and Recursion in the Box Calculus. Forthcoming Report (1992).

    Google Scholar 

  15. E.Best and J.Esparza: Model Checking of Persistent Petri Nets. Hildesheimer Informatikbericht 11/91. Proc. of Computer Science Logic 91, to appear in Springer-Verlag Lecture Notes in Computer Science (1992).

    Google Scholar 

  16. E.Best and J.Esparza (eds.): Second Progress Report of DEMON. Studien der Gesellschaft für Mathematik und Datenverarbeitung Nr.198, Sankt Augustin (August 1991).

    Google Scholar 

  17. E.Best, J.Esparza and M.Koutny: Operational Semantics of the Box Algebra. Forthcoming Technical Report.

    Google Scholar 

  18. G.Boudol: Notes on Algebraie Calculi of Processes. In: Logics and Models of Concurrent Systems (ed. K.R.Apt), 261–304 (1985).

    Google Scholar 

  19. G. Boudol and I. Castellani: Flow Models of Distributed Computations: Event Structures and Nets. Rapport de Recherche, INRIA, Sophia Antipolis (July 1991).

    Google Scholar 

  20. R.H. Campbell and N.A. Habermann: The specification of Process Synchronisation by Path Expressions. Springer-Verlag Lecture Notes in Computer Science Vol. 16, 89–102 (1974).

    Google Scholar 

  21. L.Cherkasova and V.Kotov: Descriptive and Analytical Process Algebras. Advances in Petri Nets 89 (ed. G.Rozenberg), Springer-Verlag Lecture Notes in Computer Science Vol. 424, 77–104 (1989).

    Google Scholar 

  22. P.Degano, R. De Nicola and U.Montanari: Observational equivalences for Concurrency Models. In: Formal Description of Programming Concepts III (ed. M.Wirsing), North Holland, 105–129 (1986).

    Google Scholar 

  23. P.Degano, R. De Nicola and U.Montanari: A Distributed Operational Semantics for CCS Based on C/E Systems. Acta Informatica 26 (1988).

    Google Scholar 

  24. P. Degano, R. De Nicola and U. Montanari: On the Consistency of ‘Truly Concurrent’ Operational and Denotational Semantics. Proc. 3rd Ann. Symp. on Logics in Computer Science 88, 133–141 (1988).

    Google Scholar 

  25. R.Devillers: Maximality Preservation and the ST-idea for Action Refinement. Technical Report LIT-242, Laboratoire d'Informatique Théorique, Université Libre de Bruxelles (August 1991). Also: In this Volume.

    Google Scholar 

  26. E.W.Dijkstra: An Assertional Proof of a Program by G.L.Peterson. EWD-779 (1981).

    Google Scholar 

  27. J.Esparza: Fixpoint Definition of Recursion in the Box Algebra. Memorandum, Universität Hildesheim (December 1991).

    Google Scholar 

  28. J.Fanchon: FIFO-net Model for Processes with Asynchronous Communication. Proc. 12th Int. Conference on Applications and Theory of Petri Nets, Gjern (June 1991). Also: in this volume.

    Google Scholar 

  29. H.J. Genrich and K. Lautenbach: System Modelling with High Level Petri Nets. Theoretical Computer Science 13, 109–136 (1981).

    Google Scholar 

  30. R.J. van Glabbeek and F.V. Vaandrager: Petri Net Models for Algebraic Theories of Concurrency. Proc. PARLE 89, Springer-Verlag Lecture Notes in Computer Science Vol. 259, 224–242 (1987).

    Google Scholar 

  31. U.Goltz: über die Darstellung von CCS-Programmen durch Petrinetze. (In German.) R.Oldenbourg Verlag, GMD-Bericht Nr.172 (1988). See also: U.Goltz: On Representing CCS Programs by Finite Petri Nets. Proc. MFCS-88, Springer-Verlag Lecture Notes in Computer Science Vol.324, 339–350 (1988).

    Google Scholar 

  32. U.Goltz and R.J.van Glabbeek: Refinement of Actions in Causality Based Models. Proc. of REX Workshop on Stepwise Refinement of Distributed Systems, Springer-Verlag Lecture Notes in Computer Science (1989), 267–300.

    Google Scholar 

  33. U. Goltz and R.J.van Glabbeek: Equivalences and Refinement. 18ème école de Printemps Semantique du Parallelisme, Springer-Verlag Lecture Notes in Computer Science Vol. 469, 309–333 (1990).

    Google Scholar 

  34. U.Goltz and A.Rensink: Finite Petri Nets as Models for Recursive Behaviour. Arbeitspapiere der GMD 604 (December 1991).

    Google Scholar 

  35. R.Gorrieri and U.Montanari: SCONE: a Simple Calculus of Nets. Proc. of CONCUR-90 (ed. J.Baeten and J.W.Klop), Springer-Verlag Lecture Notes in Computer Science Vol.458, 2–30 (1990).

    Google Scholar 

  36. R.J.van Glabbeek: The Refinement Theorem for ST-bisimulation Semantics. Proc. IFIP Working Conference on Programming Concepts and Methods. North Holland (1990).

    Google Scholar 

  37. M.Hack: Petri Net Languages. Technical Report 159, MIT, Laboratory of Computer Science (1976).

    Google Scholar 

  38. J.Hall: Petri Boxes and General Recursion. DEMON Technical Report, Computing Laboratory, University of Newcastle-upon-Tyne (June 1991).

    Google Scholar 

  39. J.Hall and R.P.Hopkins: PN 3—Preliminary Notions for a Petri Net Based Programming Notation: Generalised Communication. DEMON Technical Report, Computing Laboratory, University of Newcastle-upon-Tyne (June 1990/January 1991).

    Google Scholar 

  40. R.P.Hopkins, O.Botti, J.Hall: A Basic-Net Algebra for Program Semantics and its Application to occam. In this volume.

    Google Scholar 

  41. R.P.Hopkins: A (prioritised) Petri Box Algebra and its Use for a Triple Modular Redundancy Case Study. DEMON Technical Report (July 1991).

    Google Scholar 

  42. C.A.R. Hoare: Communicating Sequential Processes. CACM 21(8), 666–677 (1978).

    Google Scholar 

  43. C.A.R.Hoare: Communicating Sequential Processes. Prentice Hall (1985).

    Google Scholar 

  44. R.Janicki and P.E.Lauer: Specification and Analysis of Concurrent Systems: the COSY Approach. To appear in Springer-Verlag Monographs on Theoretical Computer Science.

    Google Scholar 

  45. K. Jensen: Coloured Petri Nets. Springer-Verlag Lecture Notes in Computer Science Vol. 254, 248–299 (1986).

    Google Scholar 

  46. P.E.Lauer: Path Expressions as Petri Nets, or Petri Nets with Fewer Tears. Memorandum MRM/70, Computing Laboratory, University of Newcastle-upon-Tyne (1974).

    Google Scholar 

  47. P.E.Lauer, E.Best and M.W.Shields: Formal Theory of the Basic COSY Notation. Technical Report 143, Computing Laboratory, University of Newcastle-upon-Tyne (1979).

    Google Scholar 

  48. D. May: occam. SIGPLAN Notices, Vbl. 18(4), pp. 69–79 (April 1983).

    Google Scholar 

  49. R.Milner: A Calculus of Communicating Systems. Springer-Verlag Lecture Notes in Computer Science Vol.84 (1980).

    Google Scholar 

  50. R.Milner: Communication and Concurrency. Prentice Hall (1989).

    Google Scholar 

  51. E.R.Olderog: Nets, Terms and Formulas. Habilitation (1989). Cambridge Tracts in Theoretical Computer Science (1991).

    Google Scholar 

  52. G.L. Peterson: Myths about the Mutual Exclusion Problem. IPL Vol. 12/3, 115–116 (1981).

    Google Scholar 

  53. A. Rabinovich and B. Trakhtenbrot: Behaviour Structure and Nets. Fundamenta Informaticae Vol. XI/4, 357–404 (1988).

    Google Scholar 

  54. W.Reisig: Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science Vol.4, Springer-Verlag (1988).

    Google Scholar 

  55. W. Reisig: Petri Nets and Algebraic Specifications. Theoretical Computer Science Vol. 80, 1–34 (1991).

    Google Scholar 

  56. G. Rozenberg and P.S. Thiagarajan: Petri Nets: Basic Notions, Structure and Behaviour. Springer-Verlag Lecture Notes in Computer Science Vol. 224, 585–8 (1986).

    Google Scholar 

  57. M.W.Shields: Concurrency. To appear in MIT Press.

    Google Scholar 

  58. R. de Simone: Higher-level Synchronising Devices in MEIJE-SCCS. Theoretical Computer Science Vol. 37, 245–267 (1985).

    Google Scholar 

  59. D.Taubner: Finite Representation of CCS and TCSP Programs by Automata and Petri Nets. Springer-Verlag Lecture Notes in Computer Science Vol. 369 (1989).

    Google Scholar 

  60. W. Vogler: Failure Semantics Based on Interval Semiwords is a Congruence for Refinement. Distributed Computing 4, 139–162 (1991).

    Google Scholar 

  61. G. Winskel: A New Definition of Morphism on Petri Nets. Proc. STACS'84, Springer-Verlag Lecture Notes in Computer Science Vol. 166, 140–150 (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Hildesheim, Marienburger Platz 22, D-3200, Hildesheim, Germany

    Eike Best

  2. Laboratoire d'Informatique Théorique, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050, Bruxelles, Belgium

    Raymond Devillers

  3. Computing Laboratory, The University of Newcastle-upon-Tyne, NE1 7RU, Newcastle-upon-Tyne, UK

    Jon G. Hall

Authors
  1. Eike Best
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raymond Devillers
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jon G. Hall
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Best, E., Devillers, R., Hall, J.G. (1992). The box calculus: A new causal algebra with multi-label communication. In: Rozenberg, G. (eds) Advances in Petri Nets 1992. Lecture Notes in Computer Science, vol 609. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55610-9_167

Download citation

  • DOI: https://doi.org/10.1007/3-540-55610-9_167

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55610-7

  • Online ISBN: 978-3-540-47258-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation