Abstract
The concatenable processes of a Petri net N can be characterized abstractly as the arrows of a symmetric monoidal category P[N]. Yet, this is only a partial axiomatization, since P[N] is built on a concrete, ad hoc chosen, category of symmetries. In this paper we give a fully equational description of the category of concatenable processes of N, thus yielding an axiomatic theory of the noninterleaving behaviour of Petri nets.
The author was supported by EU Human Capital and Mobility grant erbchbgct920005. Work partly carried out during the author's doctorate at Università di Pisa, Italy.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J. Bénabou. Categories with Multiplication. Comptes Rendue Académie Science Paris, n. 256, pp. 1887–1890, 1963.
E. Best, and R. Devillers. Sequential and Concurrent Behaviour in Petri Net Theory. Theoretical Computer Science, n. 55, pp. 87–136, 1987.
P. Degano, J. Meseguer, and U. Montanari. Axiomatizing Net Computations and Processes. In Proceedings of the 4th LICS Symposium, pp. 175–185, IEEE, 1989.
S. Eilenberg, and G.M. Kelly. Closed Categories. In Proceedings of the Conference on Categorical Algebra, La Jolla, S. Eilenberg et al., Eds., pp. 421–562, Springer, 1966.
U. Goltz, and W. Reisig. The Non-Sequential Behaviour of Petri Nets. Information and Computation, n. 57, pp. 125–147, 1983.
R. Gorrieri, and U. Montanari. Scone: A Simple Calculus of Nets. In Proceedings of CONCUR '90, LNCS n. 458, pp. 2–31, 1990.
G.M. Kelly. On MacLane's Conditions for Coherence of Natural Associativities, Commutativities, etc. Journal of Algebra, n. 1, pp. 397–402, 1964.
W. Lawvere. Functorial Semantics of Algebraic Theories. PhD Thesis, Columbia University, New York, 1963. An abstract appears in Proceedings of the National Academy of Science, n. 50, pp. 869–872, 1963.
S. MacLane. Natural Associativity and Commutativity. Rice University Studies, n. 49, pp. 28–46, 1963.
S. MacLane. Categorical Algebra. Bulletin American Mathematical Society, n. 71, pp. 40–106, 1965.
S. MacLane. Categories for the Working Mathematician. Springer-Verlag, 1971.
J. Meseguer, and U. Montanari. Petri Nets are Monoids. Information and Computation, n. 88, pp. 105–154, Academic Press, 1990.
E.H. Moore. Concerning the abstract group of order k! isomorphic with the symmetric substitution group on k letters. Proceedings of the London Mathematical Society, n. 28, PP. 357–366, 1897.
C.A. Petri. Non-Sequential Processes. Interner Bericht ISF-77-5, Gesellschaft für Mathematik und Datenverarbeitung, Bonn, Germany, 1977.
V. Sassone. On the Semantics of Petri Nets: Processes, Unfoldings and Infinite Computations. PhD Thesis TD 6/94, Dipartimento di Informatica, Università di Pisa, 1994.
V. Sassone. Some Remarks on Concatenable Processes. Technical Report TR 6/94, Dipartimento di Informatica, Università di Pisa, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sassone, V. (1995). Axiomatizing Petri net concatenable processes. In: Reichel, H. (eds) Fundamentals of Computation Theory. FCT 1995. Lecture Notes in Computer Science, vol 965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60249-6_73
Download citation
DOI: https://doi.org/10.1007/3-540-60249-6_73
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60249-1
Online ISBN: 978-3-540-44770-2
eBook Packages: Springer Book Archive