Abstract
We exploit a notion of interface for Petri nets in order to design a set of net combinators. For such a calculus of nets, we focus on the behavioural congruences arising from four simple notions of behaviour, viz., traces, maximal traces, step, and maximal step traces, and from the corresponding four notions of bisimulation, viz., weak and weak step bisimulation and their maximal versions. We characterize such congruences via universal contexts and via games, providing in such a way an understanding of their discerning powers.
Supported by EU Human Capital and Mobility grant ERBCHBGCT920005.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
S. Abramsky, and R. Jagadeesan, “Games and Full Completeness for Multiplicative Linear Logic”, Technical Report DoC 92/24, Imperial College, 1992.
E. Best, R. Devillers, and J. Hall, “The Petri Box Calculus: a New Causal Algebra with Multilabel Communication”, in Advances in Petri Nets, G. Rozenberg, Ed., LNCS n. 609, pp. 21–69, Springer-Verlag, 1992.
C. Brown, D. Gurr, and V. De. Paiva, “A Linear Specification Language for Petri Nets”, Report DAIMI PB-363, Computer Science Dept., University of Aarhus, 1991.
J. Bruno, and S.M. Altman, “A Theory of Asynchronous Control Networks”, IEEE Transactions on Computers, Vol. C-20, pp. 629–638, 1971.
P. Degano, J. Meseguer, and U. Montanari, “Axiomatizing Net Computations and Processes”, in Proceedings of the 4th LICS Symposium, pp. 175–185, IEEE Press, 1989.
J.B. Dennis, “Modular, Asynchronous Control Structures for a High Performance Processor”, in Record of the Project MAC Conference on Concurrent Systems and Parallel Computation, ACM Press, 1970.
R. Gorrieri, and U. Montanari, “Scone: A Simple Calculus of Nets”, in Proceedings of CONCUR '90, LNCS n. 458, J. Baeten, J. Klop, Eds., pp. 2–31, Springer-Verlag, 1990.
M. Hennessy, “Algebraic Theory of Processes”. MIT Press, 1988.
C.A.R. Hoare, “Communicating Sequential Processes”. Prentice Hall, 1985.
R.M. Keller, “Towards a Theory of Universal Speed-Independent Modules”, IEEE Transactions on Computers, Vol. C-23, pp. 21–33, 1974.
J. Meseguer, and U. Montanari, “Petri Nets are Monoids”, Information and Computation, n. 88, Academic Press, pp. 105–154, 1990.
R. Milner, “A Calculus of Communicating Systems”. LNCS n. 92, Springer-Verlag, 1980.
R. Milner, “Communication and Concurrency”. Prentice Hall, 1989.
R. Milner, “Action Calculi or Syntactic Action Structures”, in Proceedings of MFCS '93, LNCS n. 711, A. Borzyszkowski, S. Sokolowski, Eds., pp. 105–121, Springer-Verlag, 1993.
M. Nielsen, and C. Clausen, “Bisimulation for Models in Concurrency”, in Proceedings of CONCUR '94, LNCS n. 836, B. Jonsson, J. Parrow, Eds., pp. 385–400, Springer-Verlag, 1994.
M. Nielsen, G. Plotkin, and G. Winskel, “Petri Nets, Event Structures and Domains, Part 1”, Theoretical Computer Science, n. 13, Elsevier, pp. 85–108, 1981.
M. Nielsen, L. Priese, and V. Sassone, “An Algebra of Petri Nets”, To appear as Technical Report BRICS, RS Series, 1995.
S.S. Patil, “Limitations and Capabilities of Dijkstra's Semaphore Primitives for Coordination among Processes”, Computation Structure Group Memo n. 57, Project MAC, MIT, 1971.
L. Priese, “Automata and Concurrency”, Theoretical Computer Science, n. 25, Elsevier, pp. 221–265, 1983.
W. Reisig, “Petri Nets”. Springer-Verlag, 1985.
V. Sassone, “On the Category of Petri Net Computations”, in Proceedings of TAP-SOFT '95, P. Mosses, M. Nielsen, M.I. Schwartzbach, Eds., LNCS n. 915, pp. 334–348, Springer-Verlag, 1995.
C. Stirling, “Modal and Temporal Logics for Processes”, Notes for Summer School in Logic Methods in Concurrency, Computer Science Dept., University of Aarhus, 1993.
G. Winskel, “Petri Nets, Algebras, Morphisms and Compositionality”, Information and Computation, n. 72, Academic Press, pp. 197–238, 1987
M. Yoeli, “Petri Nets and Asynchronous Control Networks”, Report CS-73-07, Dept. of Applied Mathematics and Computer Science, University of Waterloo, 1973.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nielsen, M., Priese, L., Sassone, V. (1995). Characterizing behavioural congruences for Petri nets. In: Lee, I., Smolka, S.A. (eds) CONCUR '95: Concurrency Theory. CONCUR 1995. Lecture Notes in Computer Science, vol 962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60218-6_13
Download citation
DOI: https://doi.org/10.1007/3-540-60218-6_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60218-7
Online ISBN: 978-3-540-44738-2
eBook Packages: Springer Book Archive