Advertisement

SCONE: A simple calculus of nets

  • Roberto Gorrieri
  • Ugo Montanari
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 458)

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].

Keywords

Transition System Operational Semantic Local Choice Monoidal Category Sequential Composition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ADJ77]
    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. [As87]
    Asperti A., A Logic for Concurency, Tech. Report, Dipartimento di Informatica, November 1987.Google Scholar
  3. [AFG90]
    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. [BC89]
    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. [BD87]
    Best E., Devillers R., Sequential and Concurrent Behaviour in Petri Net Theory, Theoretical Computer Science, 55 (1), (1987), 87–136.Google Scholar
  6. [B188]
    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. [Ch89]
    Cherkasova L., Posets with Non-Actions: A Model for Concurrent Nondeterministic Processes, Arbeitspapiere der GMD n. 403, July 1989.Google Scholar
  8. [Co90]
    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. [DDM88a]
    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. [DDM88b]
    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. [DDM89]
    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. [DGM88]
    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. [DMM89]
    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. [F90]
    Ferrari G., Unifying Models for Concurrency, Ph.D. Thesis, TD 4/90, Dip. di Informatica, Pisa, March 1990.Google Scholar
  15. [FM90]
    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. [G87]
    Girard J.Y., Linear Logic, Theoretical Computer Science, 50, (1987), 1–102.Google Scholar
  17. [Go88]
    Goltz U., On Representing CCS Programs by Finite Petri Nets, Proc. MFCS'88, LNCS 324, 339–350.Google Scholar
  18. [GG89]
    Gunter C., Gehlot V., Nets as Tensor Theories, in Advances in Petri Nets 1989, LNCS 424.Google Scholar
  19. [GM84]
    Goltz U., Mycroft A., On the Relationships of CCS and Petri Nets, in Proc. 11th ICALP, LNCS, 172, 1984, 196–208.Google Scholar
  20. [GMM88]
    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. [GR83]
    Goltz U., Reisig W., The Non-sequential Behaviour of Petri Nets, Information and Co., 57, (1983), 125–147.Google Scholar
  22. [K78]
    Kotov V., An Algebra for Parallelism Based on Petri Nets, LNCS 64, 1978, 39–55.Google Scholar
  23. [MaM89]
    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. [Mil84]
    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. [Mil89]
    Milner R., Communication and Concurrency, Prentice-Hall, 1989.Google Scholar
  26. [ML71]
    Mac Lane S., Categories for the working Mathematicians, Springer-Verlag, 1971.Google Scholar
  27. [MM88]
    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. [MY89]
    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. [Old89]
    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. [Pet62]
    Petri C.A., Kommunication mit Automaten, Schriften des Institutes fur Instrumentelle Mathematik, Bonn, 1962.Google Scholar
  31. [Plo81]
    Plotkin G., A Structural Approach to Operational Semantics, Technical Report DAIMI FN-19, Aarhus University, Department of Computer Science, Aarhus, 1981.Google Scholar
  32. [T89]
    Taubner D., Finite Representation of CCS and TCSP Programs by Automata and Petri Nets, LNCS 369, 1989.Google Scholar
  33. [W85]
    Winskel G., Categories of Model of Concurrency, in Seminar on Concurrency, LNCS 197, 1985, 246–267.Google Scholar
  34. [W87]
    Winskel G., Petri Nets, Algebras, Morphisms and Compositionality, Information and Computation 72, 1987, 197–238.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Roberto Gorrieri
    • 1
  • Ugo Montanari
    • 1
  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItaly

Personalised recommendations