Abstract
In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalization of the ordinary model where some places, designated as open, represent an interface of the system towards the environment. Besides generalizing the token game to reflect this extension, we define a truly concurrent semantics for open nets by extending the Goltz-Reisig process semantics of Petri nets. We introduce a composition operation over open nets, characterized as a pushout in the corresponding category, suitable to model both interaction through open places and synchronization of transitions. The process semantics is shown to be compositional with respect to such composition operation. Technically, our result is similar to the amalgamation theorem for data-types in the framework of algebraic specifications. A possible application field of the proposed constructions and results is the modeling of interorganizational workflows, recently studied in the literature. This is illustrated by a running example.
Research partially supported by the EC TMR Network GETGRATS, by the ESPRIT Working Group APPLIGRAPH, by the MURST project TOSCA and by the DFG researcher group Petri Net Technology.
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P. Baldan, A. Corradini, H. Ehrig, and R. Heckel. Compositional modeling of reactive systems using open nets [extended version]. The paper can be downloaded at the address http://www.di.unipi.it/baldan/Papers/Soft-copy-ps/open-ext.ps.gz, 2001.
E. Best, R. Devillers, and J. G. Hall. The Petri box calculus: a new causal algebra with multi-label communication. In G. Rozemberg, editor, Advances in Petri Nets, volume 609 of LNCS, pages 21–69. Springer Verlag, 1992.
A. Corradini. Concurrent graph and term graph rewriting. In U. Montanari and V. Sassone, editors, Proceedings of CONCUR’96, volume 1119 of LNCS, pages 438–464. Springer Verlag, 1996.
H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1. Springer Verlag, Berlin, 1985.
U. Golz and W. Reisig. The non-sequential behaviour of Petri nets. Information and Control, 57:125–147, 1983.
R. Heckel. Open Graph Transformation Systems: A New Approach to the Compositional Modelling of Concurrent and Reactive Systems. PhD thesis, TU Berlin, 1998.
E. Kindler. A compositional partial order semantics for Petri net components. In P. Azema and G. Balbo, editors, Application and Theory of Petri Nets, volume 1248 of LNCS, pages 235–252. Springer Verlag, 1997.
M. Koutny and E. Best. Operational and denotational semantics for the box algebra. Theoretical Computer Science, 211(1–2):1–83, 1999.
M. Koutny, J. Esparza, and E. Best. Operational semantics for the Petri box calculus. In B. Jonsson and J. Parrow, editors, Proceedings of CONCUR’ 94, volume 836 of LNCS, pages 210–225. Springer Verlag, 1994.
J. Meseguer and U. Montanari. Petri nets are monoids. Information and Computation, 88:105–155, 1990.
M. Nielsen, G. Plotkin, and G. Winskel. Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science, 13:85–108, 1981.
M. Nielsen, L. Priese, and V. Sassone. Characterizing Behavioural Congruences for Petri Nets. In Proceedings of CONCUR’95, volume 962 of LNCS, pages 175–189. Springer Verlag, 1995.
J. Padberg, H. Ehrig, and L. Ribeiro. Algebraic high-level net transformation systems. Mathematical Structures in Computer Science, 5(2):217–256, 1995.
J. Padberg, L. Jansen, R. Heckel, and H. Ehrig. Interoperability in train control systems: Specification of scenarios using open nets. In Proc. IDPT, pages 17–28. Society for Design and Process Science, 1998.
L. Priese and H. Wimmel. A uniform approach to true-concurrency and interleaving semantics for Petri nets. Theoretical Computer Science, 206(1–2):219–256, 1998.
W. Reisig. Petri Nets: An Introduction. EACTS Monographs on Theoretical Computer Science. Springer Verlag, 1985.
W. van der Aalst. The application of Petri nets to workflow management. The Journal of Circuits, Systems and Computers, 8(1):21–66, 1998.
W. van der Aalst. Interorganizational workflows: An approach based on message sequence charts and Petri nets. System Analysis and Modeling, 34(3):335–367, 1999.
G. Winskel. Event Structures. In Petri Nets: Applications and Relationships to Other Models of Concurrency, volume 255 of LNCS, pages 325–392. Springer Verlag, 1987.
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Baldan, P., Corradini, A., Ehrig, H., Heckel, R. (2001). Compositional Modeling of Reactive Systems Using Open Nets. In: Larsen, K.G., Nielsen, M. (eds) CONCUR 2001 — Concurrency Theory. CONCUR 2001. Lecture Notes in Computer Science, vol 2154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44685-0_34
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DOI: https://doi.org/10.1007/3-540-44685-0_34
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