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.
Preview
Unable to display preview. Download preview PDF.
References
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.
Asperti A., A Logic for Concurency, Tech. Report, Dipartimento di Informatica, November 1987.
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.
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.
Best E., Devillers R., Sequential and Concurrent Behaviour in Petri Net Theory, Theoretical Computer Science, 55 (1), (1987), 87–136.
Blanco C., Hacer Explícita la Elección Atómica de CCS Facilita la Construcción de Ordenes Parciales, Master thesis, ESLAI, Buenos Aires, December 1988.
Cherkasova L., Posets with Non-Actions: A Model for Concurrent Nondeterministic Processes, Arbeitspapiere der GMD n. 403, July 1989.
Corradini A., An Algebraic Semantics for Transition Systems and Logic Programming, Ph.D. Thesis, TD 8/90, Dipartimento di Informatica, Pisa, March 1990.
Degano P., De Nicola R., Montanari U., A Distributed Operational Semantics for CCS based on Condition/Event Systems, Acta Informatica, 26 (1988), 59–91.
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.
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.
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.
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.
Ferrari G., Unifying Models for Concurrency, Ph.D. Thesis, TD 4/90, Dip. di Informatica, Pisa, March 1990.
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.
Girard J.Y., Linear Logic, Theoretical Computer Science, 50, (1987), 1–102.
Goltz U., On Representing CCS Programs by Finite Petri Nets, Proc. MFCS'88, LNCS 324, 339–350.
Gunter C., Gehlot V., Nets as Tensor Theories, in Advances in Petri Nets 1989, LNCS 424.
Goltz U., Mycroft A., On the Relationships of CCS and Petri Nets, in Proc. 11th ICALP, LNCS, 172, 1984, 196–208.
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).
Goltz U., Reisig W., The Non-sequential Behaviour of Petri Nets, Information and Co., 57, (1983), 125–147.
Kotov V., An Algebra for Parallelism Based on Petri Nets, LNCS 64, 1978, 39–55.
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.
Milner R., A Complete Inference System for a Class of Regular Behaviours, Journal of Computer and System Sciences, 28, (1984), 439–466.
Milner R., Communication and Concurrency, Prentice-Hall, 1989.
Mac Lane S., Categories for the working Mathematicians, Springer-Verlag, 1971.
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.
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.
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.
Petri C.A., Kommunication mit Automaten, Schriften des Institutes fur Instrumentelle Mathematik, Bonn, 1962.
Plotkin G., A Structural Approach to Operational Semantics, Technical Report DAIMI FN-19, Aarhus University, Department of Computer Science, Aarhus, 1981.
Taubner D., Finite Representation of CCS and TCSP Programs by Automata and Petri Nets, LNCS 369, 1989.
Winskel G., Categories of Model of Concurrency, in Seminar on Concurrency, LNCS 197, 1985, 246–267.
Winskel G., Petri Nets, Algebras, Morphisms and Compositionality, Information and Computation 72, 1987, 197–238.
Author information
Authors and Affiliations
Editor information
Rights 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