Towards a Standard for Modular Petri Nets: A Formalisation

When designing complex systems, mechanisms for structuring, composing, and reusing system components are crucial. Today, there are many approaches for equipping Petri nets with such mechanisms. In the context of defining a standard interchange format for Petri nets, modular PNML was defined as a mechanism for modules in Petri nets that is independent from a particular version of Petri nets and that can mimic many composition mechanisms by a simple import and export concept. Due to its generality, the semantics of modular PNML was only informally defined. Moreover, modular PNML did not define which concepts could or should be subject to import and export in high-level Petri nets. In this paper, we formalise a minimal version of modular high-level Petri nets, which is based on the concepts of modular PNML. This shows that modular PNML can be formalised once a specific version of Petri net is fixed. Moreover, we present and discuss some more advanced features of modular Petri nets that could be included in the standard. This way, we provide a formal foundation and a basis for a discussion of features to be included in the upcoming standard of a module concept for Petri nets in general and for high-level nets in particular.

[1]  Jonathan Billington,et al.  Many-sorted high-level nets , 1989, Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89.

[2]  Wolfgang Reisig,et al.  Petri Nets and Algebraic Specifications , 1991, Theor. Comput. Sci..

[3]  Laure Petrucci,et al.  A Modelling Approach with Coloured Petri Nets , 2008, Ada-Europe.

[4]  Kurt Jensen,et al.  Coloured Petri Nets: Basic Concepts, Analysis Methods and Practical Use. Vol. 2, Analysis Methods , 1992 .

[5]  Laure Petrucci,et al.  Modular Analysis of Petri Nets , 2000, Comput. J..

[6]  Ekkart Kindler.  Modular PNML revisited: Some ideas for strict typing , 2007 .

[7]  Jacques Vautherin,et al.  Parallel systems specitications with coloured Petri nets and algebraic specifications , 1986, European Workshop on Applications and Theory of Petri Nets.

[8]  Gianfranco Balbo,et al.  Application and Theory of Petri Nets 1997 , 1997 .

[9]  Paul Grefen,et al.  A Three-Level Process Framework for Contract-Based Dynamic Service Outsourcing , 2003 .

[10]  Giovanni Chiola,et al.  On Well-Formed Coloured Nets and Their Symbolic Reachability Graph , 1991 .

[11]  Jiacun Wang,et al.  Timed Petri Nets: Theory and Application , 1998 .

[12]  Grzegorz Rozenberg.  Advances in Petri Nets 1987 , 1986, Lecture Notes in Computer Science.

[13]  Tullio Vardanega,et al.  Reliable Software Technologies - Ada-Europe 2008, 13th Ada-Europe International Conference on Reliable Software Technologies, Venice, Italy, June 16-20, 2008. Proceedings , 2008, Ada-Europe.

[14]  Ekkart Kindler,et al.  The Petri Net Markup Language , 2003, Petri Net Technology for Communication-Based Systems.

[15]  Jonathan Billington,et al.  8.3.1 A New Graphical Systems Engineering International Standard: ISO/IEC 15909 for High‐level Petri Nets , 2001 .

[16]  Karsten Schmidt.  Verification of Siphons and Traps for Algebraic Petri Nets , 1997 .

[17]  Hartmut Ehrig,et al.  Fundamentals of Algebraic Specification 1: Equations and Initial Semantics , 1985 .

[18]  Ekkart Kindler,et al.  A Universal Module Concept for Petri Nets - an implementation-oriented approach , 2001 .

[19]  Karsten Wolf.  Verification of Siphons and Traps for Algebraic Petri Nets , 1997, ICATPN.

[20]  Lars Michael Kristensen,et al.  Coloured Petri Nets and CPN Tools for modelling and validation of concurrent systems , 2007, International Journal on Software Tools for Technology Transfer.