Abstract
We introduce ranked open nets, a reactive extension of Petri nets which generalises a basic open net model introduced in a previous work by allowing for a refined notion of interface. The interface towards the external environment of a ranked open net is given by a subset of places designated as open and used for composition. Additionally, a bound on the number of connections which are allowed on an open place can be specified. We show that the non-deterministic process semantics is compositional with respect to the composition operation over ranked open nets, a result which did not hold for basic open nets.
Supported by the MIUR Project ART, the DFG project Behaviour-GT and CRUI/DAAD Vigoni.
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Baldan, P., Corradini, A., Ehrig, H., Heckel, R.: Compositional semantics for open Petri nets based on deterministic processes. Mathematical Structures in Computer Science 15(1), 1–35 (2005)
Baldan, P., Corradini, A., Ehrig, H., Heckel, R., König, B.: Bisimilarity and behaviour-preserving reconfigurations of open Petri nets. In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds.) CALCO 2007. LNCS, vol. 4624, pp. 126–142. Springer, Heidelberg (2007)
Basten, T.: In terms of nets: System design with Petri nets and process algebra. PhD thesis, Eindhoven University of Technology (1998)
Bonchi, F., Brogi, A., Corfini, S., Gadducci, F.: A behavioural congruence for web services. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 240–256. Springer, Heidelberg (2007)
Corradini, A., Montanari, U., Rossi, F.: Graph processes. Fundamenta Informaticae 26, 241–265 (1996)
Desel, J., Juhás, G., Neumair, C.: Finite unfoldings of unbounded Petri nets. In: Cortadella, J., Reisig, W. (eds.) ICATPN 2004. LNCS, vol. 3099, pp. 157–176. Springer, Heidelberg (2004)
Ehrig, H., König, B.: Deriving bisimulation congruences in the DPO approach to graph rewriting. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 151–166. Springer, Heidelberg (2004)
Heckel, R.: Open Graph Transformation Systems: A New Approach to the Compositional Modelling of Concurrent and Reactive Systems. PhD thesis, Technische Universität Berlins (1998)
Kindler, E.: A compositional partial order semantics for Petri net components. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 235–252. Springer, Heidelberg (1997)
McMillan, K.L.: Using unfoldings to avoid the state explosion problem in the verification of asynchronous circuits. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 164–174. Springer, Heidelberg (1993)
Milner, R.: Bigraphical reactive systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 16–35. Springer, Heidelberg (2001)
Nielsen, M., Priese, L., Sassone, V.: Characterizing Behavioural Congruences for Petri Nets. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 175–189. Springer, Heidelberg (1995)
Priese, L., Wimmel, H.: A uniform approach to true-concurrency and interleaving semantics for Petri nets. Theoretical Computer Science 206(1–2), 219–256 (1998)
Reisig, W.: Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1985)
Sassone, V., Sobociński, P.: A congruence for Petri nets. In: Proc. of PNGT 2004. ENTCS, pp. 107–120. Elsevier, Amsterdam (2005)
van der Aalst, W.: The application of Petri nets to workflow management. The Journal of Circuits, Systems and Computers 8(1), 21–66 (1998)
van der Aalst, W.: Interorganizational workflows: An approach based on message sequence charts and Petri nets. System Analysis and Modeling 34(3), 335–367 (1999)
Zhang, G., Meng, F., Jiang, C., Pang, J.: Using Petri Net to Reason with Rule and OWL. In: Proc. of CIT 2006, IEEE Computer Society Press, Los Alamitos (2006)
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Baldan, P., Corradini, A., Ehrig, H., König, B. (2008). Open Petri Nets: Non-deterministic Processes and Compositionality. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds) Graph Transformations. ICGT 2008. Lecture Notes in Computer Science, vol 5214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87405-8_18
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DOI: https://doi.org/10.1007/978-3-540-87405-8_18
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