Process Semantics of P/T-Nets with Inhibitor Arcs

In this paper, we define a process semantics of P/T-nets with inhibitor arcs (PTI-nets). For PTI-nets with bounded inhibiting places, we combine the existing approaches for ordinary P/T-nets and for elementary net systems with inhibitor arcs. To deal with unbounded inhibiting places, a new feature has to be added to the underlying occurrence nets. In either case we show how to construct a process from a step sequence and give a complete characterization of all processes which can be obtained in this way. Using these processes it is possible to express the causal relationships between events in a PTI-net behaviour.

[1]  Maciej Koutny,et al.  Order Structures and Generalisations of Szpilrajn's Theorem , 1993, FSTTCS.

[2]  Neil D. Jones,et al.  A Precise Version of a Time Hierarchy Theorem , 1999, Fundam. Informaticae.

[3]  Haim Gaifman,et al.  Partial Order Models of Concurrency and the Computation of Functions , 1987, LICS.

[4]  Maciej Koutny,et al.  Semantics of Inhibitor Nets , 1995, Inf. Comput..

[5]  James Lyle Peterson,et al.  Petri net theory and the modeling of systems , 1981 .

[6]  G. Michele Pinna,et al.  Process Semantics for Place/Transition Nets with Inhibitor and Read Arcs , 1999, Fundam. Informaticae.

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

[8]  Joost Engelfriet,et al.  Elementary Net Systems , 1996, Applications and Theory of Petri Nets.

[9]  E. Szpilrajn Sur l'extension de l'ordre partiel , 1930 .

[10]  Maciej Koutny,et al.  Structure of Concurrency , 1991, Theor. Comput. Sci..

[11]  Wolfgang Reisig,et al.  Lectures on Petri Nets I: Basic Models , 1996, Lecture Notes in Computer Science.

[12]  Maciej Koutny,et al.  Fundamentals of modelling concurrency using discrete relational structures , 1997, Acta Informatica.

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

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

[15]  Roland Fraïssé Theory of relations , 1986 .

[16]  Walter Vogler Partial order semantics and read arcs , 2002, Theor. Comput. Sci..

[17]  Eike Best,et al.  Nonsequential Processes: A Petri Net View , 1988 .

[18]  Maciej Koutny,et al.  On Causality Semantics of Nets with Priorities , 1999, Fundam. Informaticae.