Skip to main content

SCONE: A simple calculus of nets

  • Invited Lectures
  • Conference paper
  • First Online:
CONCUR '90 Theories of Concurrency: Unification and Extension (CONCUR 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 458))

Included in the following conference series:

Abstract

A simple calculus of Place/Transition Petri Nets, called SCONE, is introduced. Relationships between SCONE and the subset of CCS without restriction and relabelling, called RCCS, are studied by showing that RCCS can be implemented onto the net calculus. The implementation is given by means of a suitable mapping from RCCS transitions to SCONE computations, resulting in a finite net representation for RCCS agents. By quotienting the transition system of RCCS with respect to the implementation mapping, we induce also a "true concurrent" semantics for RCCS. These results are developed in the framework of "graphs with algebraic structure" as explained in [MM88, DMM89, MY89, F90, FM90, Co90].

Research supported in part by EEC Basic Research Action n.3011 CEDISYS.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gougen J.A., Tatcher J.W., Wagner E.G., Wright J.B., Initial Algebra Semantics and Continuous Algebras, Journal of the ACM, 24(1), (1977), 68–95.

    Google Scholar 

  2. Asperti A., A Logic for Concurency, Tech. Report, Dipartimento di Informatica, November 1987.

    Google Scholar 

  3. Asperti A., Ferrari G., Gorrieri R., Implicative formulae in the “Proofs as Computations” Analogy, in Proc. 17th ACM Symp. on Principles of Programming Lang. (POPL'90), San Francisco, January 1990, 59–71.

    Google Scholar 

  4. Boudol G., Castellani I., Permutation of Transitions: An Event Structure Semantics for CCS, Proc. REX School: Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, LNCS 354, 1989, 411–427.

    Google Scholar 

  5. Best E., Devillers R., Sequential and Concurrent Behaviour in Petri Net Theory, Theoretical Computer Science, 55 (1), (1987), 87–136.

    Google Scholar 

  6. Blanco C., Hacer Explícita la Elección Atómica de CCS Facilita la Construcción de Ordenes Parciales, Master thesis, ESLAI, Buenos Aires, December 1988.

    Google Scholar 

  7. Cherkasova L., Posets with Non-Actions: A Model for Concurrent Nondeterministic Processes, Arbeitspapiere der GMD n. 403, July 1989.

    Google Scholar 

  8. Corradini A., An Algebraic Semantics for Transition Systems and Logic Programming, Ph.D. Thesis, TD 8/90, Dipartimento di Informatica, Pisa, March 1990.

    Google Scholar 

  9. Degano P., De Nicola R., Montanari U., A Distributed Operational Semantics for CCS based on Condition/Event Systems, Acta Informatica, 26 (1988), 59–91.

    Google Scholar 

  10. Degano P., De Nicola R., Montanari U., Partial Ordering Semantics for CCS, Internal Report 88-3, Dipartimento di Informatica, Univ. Pisa, 1988, to appear in Theoretical Computer Science.

    Google Scholar 

  11. Degano P., De Nicola R., Montanari U., Partial Ordering Description of Nondeterministic Concurrent Systems, in Proc. REX School: Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, LNCS 354, 1989, 438–466.

    Google Scholar 

  12. Degano P., Gorrieri R., Marchetti S., An Exercise in Concurrency: A CSP Process as a Condition/Event System, in Advances in Petri Nets 1988, LNCS 340, 1988, 85–105.

    Google Scholar 

  13. Degano P., Meseguer J., Montanari U., Axiomatizing Net Computations and Processes, in Proc. Logic in Computer Science (LICS '89), Asilomar, 1989, 175–185. Extended and revised version available as technical report of Dipartimento di Informatica, Pisa University.

    Google Scholar 

  14. Ferrari G., Unifying Models for Concurrency, Ph.D. Thesis, TD 4/90, Dip. di Informatica, Pisa, March 1990.

    Google Scholar 

  15. Ferrari G., Montanari U., Towards the Unification of Models for Concurrency, in Proc. Coll. on Algebra and Trees in Prog. (CAAP'90), Copenhagen, LNCS 431, 162–176.

    Google Scholar 

  16. Girard J.Y., Linear Logic, Theoretical Computer Science, 50, (1987), 1–102.

    Google Scholar 

  17. Goltz U., On Representing CCS Programs by Finite Petri Nets, Proc. MFCS'88, LNCS 324, 339–350.

    Google Scholar 

  18. Gunter C., Gehlot V., Nets as Tensor Theories, in Advances in Petri Nets 1989, LNCS 424.

    Google Scholar 

  19. Goltz U., Mycroft A., On the Relationships of CCS and Petri Nets, in Proc. 11th ICALP, LNCS, 172, 1984, 196–208.

    Google Scholar 

  20. Gorrieri R., Marchetti S., Montanari U., A2CCS: Atomic Actions for CCS, in Proc. Coll. on Trees and Algebras in Prog. (CAAP'88), LNCS 299, 1988, 258–270. Extended version to appear in Theoretical Computer Science, 72, (1990).

    Google Scholar 

  21. Goltz U., Reisig W., The Non-sequential Behaviour of Petri Nets, Information and Co., 57, (1983), 125–147.

    Google Scholar 

  22. Kotov V., An Algebra for Parallelism Based on Petri Nets, LNCS 64, 1978, 39–55.

    Google Scholar 

  23. Martì-Oliet N., Meseguer J., From Petri Nets to Linear Logic, in Proc. 3rd Conf. on Category Theory in Computer Science, Manchester, LNCS 389, 1989, 313–340.

    Google Scholar 

  24. Milner R., A Complete Inference System for a Class of Regular Behaviours, Journal of Computer and System Sciences, 28, (1984), 439–466.

    Google Scholar 

  25. Milner R., Communication and Concurrency, Prentice-Hall, 1989.

    Google Scholar 

  26. Mac Lane S., Categories for the working Mathematicians, Springer-Verlag, 1971.

    Google Scholar 

  27. Meseguer J., Montanari U., Petri Nets are Monoids: A New Algebraic Foundation for Net Theory, in Proc. Logic in Computer Science, Edinburgh, 1988, 155–164. Full version to appear in Info. and Co, also available as Tech. Rep. SRI-CSL-88-3, SRI International, January 1988.

    Google Scholar 

  28. Montanari U., Yankelevich D., An Algebraic View of Interleaving and Distributed Operational Semantics for CCS, in Proc. 3rd Conf. on Category Theory in Comp. Scien., Manchester, LNCS 389, 1989, 5–20.

    Google Scholar 

  29. Olderog E.-R., Strong Bisimilarity on Nets. in Proc. REX School: Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, LNCS 354, 1989, 549–573.

    Google Scholar 

  30. Petri C.A., Kommunication mit Automaten, Schriften des Institutes fur Instrumentelle Mathematik, Bonn, 1962.

    Google Scholar 

  31. Plotkin G., A Structural Approach to Operational Semantics, Technical Report DAIMI FN-19, Aarhus University, Department of Computer Science, Aarhus, 1981.

    Google Scholar 

  32. Taubner D., Finite Representation of CCS and TCSP Programs by Automata and Petri Nets, LNCS 369, 1989.

    Google Scholar 

  33. Winskel G., Categories of Model of Concurrency, in Seminar on Concurrency, LNCS 197, 1985, 246–267.

    Google Scholar 

  34. Winskel G., Petri Nets, Algebras, Morphisms and Compositionality, Information and Computation 72, 1987, 197–238.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

J. C. M. Baeten J. W. Klop

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gorrieri, R., Montanari, U. (1990). SCONE: A simple calculus of nets. In: Baeten, J.C.M., Klop, J.W. (eds) CONCUR '90 Theories of Concurrency: Unification and Extension. CONCUR 1990. Lecture Notes in Computer Science, vol 458. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039047

Download citation

  • DOI: https://doi.org/10.1007/BFb0039047

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53048-0

  • Online ISBN: 978-3-540-46395-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics