On Causal Semantics of Petri Nets (extended abstract)

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van Glabbeek, Robert; Goltz, Ursula; Schicke, Jens-Wolfhard

van Glabbeek, Robert; Goltz, Ursula; Schicke, Jens-Wolfhard


2011-09-05


Conference Material


22nd International Conference on Concurrency Theory


Aachen, Germany


43-59


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 well-known 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.


Springer


Concurrency, Petri nets, PT-systems, causal semantics, processes.


http://concur2011.rwth-aachen.de/concur2011


0302-9743


nicta:5004


van Glabbeek, Robert; Goltz, Ursula; Schicke, Jens-Wolfhard. On Causal Semantics of Petri Nets (extended abstract). In: Joost-Pieter Katoen and Barbara K├Ânig Editor, editor/s. 22nd International Conference on Concurrency Theory; Aachen, Germany. Springer; 2011-09-05. 43-59.



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