Abstract
In this paper we define partial order semantics of types of nets. Types of nets are a parametric definition of Petri nets originally developed for a general presentation of the synthesis of Petri nets from (step) transition systems. Partial order semantics of a concrete net (of a certain type) usually are given by the set of labelled partial orders (LPOs) enabled w.r.t. the net. For classical place/transition nets there are several equivalent characterizations of enabled LPOs. We discuss in which way the general notion of types of nets has to be restricted such that these characterizations can also be formulated for nets of such type. In particular we consider under which requirements enabled LPOs can be defined through token flows, which have been proven to be useful for efficient synthesis and verification of Petri nets. The presented concepts form the basis for a general presentation of the synthesis of Petri nets from sets of LPOs.
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References
Badouel, E., Bednarczyk, M.A., Darondeau, P.: Generalized Automata and Their Net Representations. In: Ehrig, H., Juhás, G., Padberg, J., Rozenberg, G. (eds.) APN 2001. LNCS, vol. 2128, pp. 304–345. Springer, Heidelberg (2001)
Badouel, E., Darondeau, P.: Dualities Between Nets and Automata Induced by Schizophrenic Objects. In: Johnstone, P.T., Rydeheard, D.E., Pitt, D.H. (eds.) CTCS 1995. LNCS, vol. 953, pp. 24–43. Springer, Heidelberg (1995)
Badouel, E., Darondeau, P.: On the Synthesis of General Petri Nets. Technical Report 3025, Inria (1996)
Badouel, E., Darondeau, P.: Theory of Regions. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 529–586. Springer, Heidelberg (1998)
Bergenthum, R., Desel, J., Lorenz, R., Mauser, S.: Synthesis of Petri Nets from Finite Partial Languages. Fundam. Inform (to appear, 2008)
Bergenthum, R., Mauser, S.: Comparison of Different Algorithms to Synthesize a Petri Net from a Partial Language. In: Proceedings of Workshop CHINA @ICATPN (2008)
Desel, J., Juhás, G., Lorenz, R.: Petri Nets over Partial Algebra. In: Ehrig, H., Juhás, G., Padberg, J., Rozenberg, G. (eds.) APN 2001. LNCS, vol. 2128, pp. 126–172. Springer, Heidelberg (2001)
Droste, M., Shortt, R.M.: From Petri Nets to Automata with Concurrency. Applied Categorical Structures 10(2), 173–191 (2002)
Ehrenfeucht, A., Rozenberg, G.: Partial (set) 2-Structures. Part I: Basic Notions and the Representation Problem / Part II: State Spaces of Concurrent Systems. Acta Inf. 27(4), 315–368 (1989)
Juhás, G., Lorenz, R., Desel, J.: Can I Execute My Scenario in Your Net? In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 289–308. Springer, Heidelberg (2005)
Juhás, G., Lorenz, R., Mauser, S.: Examples and Proofs: Partial Order Semantics of Types of Nets. Technical report (2008), http://www.ku-eichstaett.de/Fakultaeten/MGF/Informatik/Mitarbeiter/Mauser/Publikationen.de
Kiehn, A.: On the Interrelation Between Synchronized and Non-Synchronized Behaviour of Petri Nets. Elektronische Informationsverarbeitung und Kybernetik 24(1/2), 3–18 (1988)
Lorenz, R., Juhás, G., Mauser, S.: How to Synthesize Nets from Languages - a Survey. In: Proceedings of the Wintersimulation Conference (WSC), pp. 637–647 (2007)
Lorenz, R., Mauser, S., Bergenthum, R.: Theory of Regions for the Synthesis of Inhibitor Nets from Scenarios. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN 2007. LNCS, vol. 4546, pp. 342–361. Springer, Heidelberg (2007)
Mazurkiewicz, A.: Petri Nets Without Tokens. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN 2007. LNCS, vol. 4546, pp. 20–23. Springer, Heidelberg (2007)
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Lorenz, R., Juhás, G., Mauser, S. (2009). Partial Order Semantics of Types of Nets. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds) SOFSEM 2009: Theory and Practice of Computer Science. SOFSEM 2009. Lecture Notes in Computer Science, vol 5404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95891-8_36
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DOI: https://doi.org/10.1007/978-3-540-95891-8_36
Publisher Name: Springer, Berlin, Heidelberg
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