Unifying Petri Nets with Restricted Occurrence Rule Using Partial Algebra

Abstract The aim of this paper is to present a unifying concept for Petri nets with restricted occurrence rule, to obtain non-sequential semantics in a systematic way. It is shown that partial algebra is a suitable basis for process construction. Restrictions of the occurrence rule are translated into restrictions of concurrent composition of processes. We illustrate this claim on several well-known examples, including context and capacity restrictions. For elementary nets with context we show the one-to-one correspondence between processes constructed using partial algebra and partial order based processes.

[1]  Józef Winkowski.  An Algebraic Description of System Behaviours , 1982, Theor. Comput. Sci..

[2]  Jörg Desel,et al.  Petri Nets over Partial Algebra , 2001, Unifying Petri Nets.

[3]  Hartmut Ehrig,et al.  Unifying Petri Nets: Advances in Petri Nets , 2002 .

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

[5]  Julia Padberg,et al.  Classification of Petri Nets Using Adjoint Functors , 2001, Bull. EATCS.

[6]  Jörg Desel,et al.  ''What Is a Petri Net?'' , 2001, Unifying Petri Nets.

[7]  José Meseguer,et al.  Axiomatizing the algebra of net computations and processes , 1996, Acta Informatica.

[8]  Jörg Desel,et al.  Process Semantics of Petri Nets over Partial Algebra , 2000, ICATPN.

[9]  Hartmut Ehrig,et al.  Parameterized Net Classes: A Uniform Approach to Petri Net Classes , 2001, Unifying Petri Nets.

[10]  Vladimiro Sassone,et al.  An axiomatization of the category of Petri net computations , 1998, Mathematical Structures in Computer Science.

[11]  Ekkart Kindler,et al.  The Dimensions of Petri Nets: The Petri Net Cube , 1998, Bull. EATCS.

[12]  Maciej Koutny,et al.  Process Semantics of P/T-Nets with Inhibitor Arcs , 2000, ICATPN.

[13]  Julia Padberg,et al.  Abstract Petri nets - uniform approach and rule-based refinement , 1996, Berichte aus der Informatik.

[14]  Roberto Bruni,et al.  Algebraic Models for Contextual Nets , 2000, ICALP.

[15]  Wolfgang Reisig,et al.  Place or Transition Petri Nets , 1996, Petri Nets.

[16]  Józef Winkowski,et al.  Behaviours of Concurrent Systems , 1980, Theor. Comput. Sci..

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

[18]  José Meseguer,et al.  Petri Nets Are Monoids , 1990, Inf. Comput..

[19]  Hans-Michael Hanisch,et al.  A Signal Extension for Petri Nets and its Use in Controller Design , 2000, Fundam. Informaticae.

[20]  Gabriel Juhás,et al.  Reasoning about Algebraic Generalisation of Petri Nets , 1999, ICATPN.

[21]  Roberto Bruni,et al.  A Comparison of Petri Net Semantics under the Collective Token Philosophy , 1998, ASIAN.

[22]  Fabio Gadducci,et al.  Axioms for Contextual Net Processes , 1998, ICALP.

[23]  Raymond R. Devillers.  The semantics of capacities in P/T nets , 1988, European Workshop on Applications and Theory in Petri Nets.