On Causal Semantics of Petri Nets
We consider approaches for causal semantics of Petri nets, explicitly representing dependencies between transition occurrences. For one-safe nets or condition/event-systems, the notion of process as defined by Carl Adam Petri provides a notion of a run of a system where causal dependencies are reflected in terms of a partial order. A wellknown problem is how to generalise this notion for nets where places may carry several tokens. Goltz and Reisig have defined such a generalisation by distinguishing tokens according to their causal history. However, this so-called individual token interpretation is often considered too detailed. A number of approaches have tackled the problem of defining a more abstract notion of process, thereby obtaining a so-called collective token interpretation. Here we give a short overview on these attempts and then identify a subclass of Petri nets, called structural conflict nets, where the interplay between conflict and concurrency due to token multiplicity does not occur. For this subclass, we define abstract processes as equivalence classes of Goltz-Reisig processes. We justify this approach by showing that we obtain exactly one maximal abstract process if and only if the underlying net is conflict-free with respect to a canonical notion of conflict.
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- [BD87]Best, E., Devillers, R.R.: Sequential and concurrent behaviour in Petri net theory. Theoretical Computer Science 55(1), 87–136 (1987), doi:10.1016/0304-3975(87)90090-9; See also: Best, E., Devillers, R.R.: Interleaving and Partial Orders in Concurrency: A Formal Comparison. In: Wirsing, M. (ed.) Formal Description of Programming Concepts III, pp. 299–321. North-Holland, Amsterdam (1987)MathSciNetCrossRefMATHGoogle Scholar
- [BMO09]Barylska, K., Mikulski, Ł., Ochmański, E.: Nonviolence Petri Nets. In: Proceedings Workshop on Concurrency, Specification and Programming, CS&P, pp. 50–59 (2009)Google Scholar
- [DMM89]Degano, P., Meseguer, J., Montanari, U.: Axiomatizing Net Computations and Processes. In: Proceedings Fourth Annual Symposium on Logic in Computer Science, LICS 1989, pp. 175–185. IEEE, Pacific Grove (1989); see also Degano, P., Meseguer, J., Montanari, U.: Axiomatizing Net Computations and Processes. Acta Informatica 33(5), 641–667 (1996), doi:10.1007/BF03036469Google Scholar
- [GGS11b]van Glabbeek, R.J., Goltz, U., Schicke, J.-W.: On Causal Semantics of Petri Nets. Technical Report 2011-06, TU Braunschweig (2011)Google Scholar
- [Gol86]Goltz, U.: How Many Transitions may be in Conflict? Petri Net Newsletter 25, 4–9 (1986)Google Scholar
- [GP95]van Glabbeek, R.J., Plotkin, G.D.: Configuration Structures (extended abstract). In: Kozen, D. (ed.) Proceedings LICS 1995, pp. 199–209 (1995); See also van Glabbeek, R.J., Plotkin, G.D.: Configuration Structures, Event Structures and Petri Nets. Theoretical Computer Science 410(41), 4111–4159, doi:10.1016/j.tcs.2009.06.014 (2009)Google Scholar
- [MM88]Meseguer, J., Montanari, U.: Petri Nets Are Monoids: A New Algebraic Foundation for Net theory. In: Proceedings Third Annual Symposium on Logic in Computer Science, LICS 1988, Edinburgh, Scotland, pp. 155–164. IEEE, Los Alamitos (1988)Google Scholar
- [Och89]Ochmański, E.: Personal communication (1989)Google Scholar
- [Pet77]Petri, C.A.: Non-sequential Processes. GMD-ISF Report 77.05, GMD (1977)Google Scholar