Compositional Modeling of Reactive Systems Using Open Nets
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.
Unable to display preview. Download preview PDF.
- 1.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.
- 2.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.Google Scholar
- 3.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.Google Scholar
- 6.R. Heckel. Open Graph Transformation Systems: A New Approach to the Compositional Modelling of Concurrent and Reactive Systems. PhD thesis, TU Berlin, 1998.Google Scholar
- 7.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.Google Scholar
- 9.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.Google Scholar
- 12.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.Google Scholar
- 14.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.Google Scholar
- 16.W. Reisig. Petri Nets: An Introduction. EACTS Monographs on Theoretical Computer Science. Springer Verlag, 1985.Google Scholar
- 19.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.Google Scholar