A Trace Semantics for Petri Nets

A generalization of the notion of trace is proposed. This enables us to associate with each Petri net a single behavioural object, namely a poset of (generalized) traces. A characterization is given of the trace languages defined by Petri nets. We show that the general event structures of Winskel and the stable event structures can also be characterized in terms of our trace languages. One consequence is that in this framework, stable event structures, general event structures, and Petri nets constitute a strictly ascending chain in terms of expressive power.

[1]  Madhavan Mukund.  Petri Nets and Step Transition Systems , 1992, Int. J. Found. Comput. Sci..

[2]  Wolfgang Reisig,et al.  The Non-sequential Behavior of Petri Nets , 1983, Inf. Control..

[3]  Grzegorz Rozenberg,et al.  Elementary Transition Systems , 1990, Theor. Comput. Sci..

[4]  Ugo Montanari,et al.  Axiomatizing net computations and processes , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[5]  Raymond R. Devillers,et al.  Sequential and Concurrent Behaviour in Petri Net Theory , 1987, Theor. Comput. Sci..

[6]  Grzegorz Rozenberg,et al.  Theory of Traces , 1988, Theor. Comput. Sci..

[7]  P. W. Hoogers,et al.  Behavioural Aspects of Petri Net , 1994 .

[8]  Grzegorz Rozenberg,et al.  Transition Systems, Event Structures and Unfoldings , 1991, Inf. Comput..

[9]  A. Arnold,et al.  An extension of the notions of traces and of asynchronous automata , 1991, RAIRO Theor. Informatics Appl..

[10]  P. S. Thiagarajan,et al.  Local Event Structures and Petri Nets , 1993, CONCUR.

[11]  Walter Vogler,et al.  A generalization of traces , 1991, RAIRO Theor. Informatics Appl..

[12]  Wolfgang Reisig,et al.  CSP-programs with individual tokens , 1984, European Workshop on Applications and Theory in Petri Nets.

[13]  Walter Vogler,et al.  Representation of a swapping class by one net , 1988, European Workshop on Applications and Theory in Petri Nets.

[14]  Glynn Winskel,et al.  Petri Nets, Algebras, Morphisms, and Compositionality , 1987, Inf. Comput..

[15]  Glynn Winskel,et al.  Petri Nets, Event Structures and Domains , 1979, Semantics of Concurrent Computation.

[16]  Antoni W. Mazurkiewicz,et al.  Concurrency, Modularity, and Synchronization , 1989, MFCS.

[17]  Eike Best,et al.  Nonsequential Processes , 1988, EATCS Monographs on Theoretical Computer Science.

[18]  Alan Mycroft,et al.  On the Relationship of CCS and Petri Nets , 1984, ICALP.