Conceptual Modeling of Concurrent Systems through Stepwise Abstraction and Refinement Using Petri Net Morphisms

Development of complex concurrent systems is very often performed in a top-down or bottom-up approach depending on design circumstances. Such design reflects vertical conceptual modeling of concurrent systems with certain number of abstraction/ refinement layers. Petri net morphisms have been proven to be useful in this process as long as certain desired structural and behavioral properties of such systems are preserved. We use example of a renting agency to illustrate applicability of morphisms in systematic development of distributed systems. Preservation of structural and behavioral properties of Petri net morphisms is also discussed.

[1]  Charles Lakos,et al.  Composing Abstractions of Coloured Petri Nets , 2000, ICATPN.

[2]  Claudia Ermel,et al.  Rule-based refinement of high-level nets preserving safety properties , 2001, Sci. Comput. Program..

[3]  Wolfgang Reisig,et al.  Distributed algorithms: modeling and analysis with Petri nets , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[4]  Jörg Desel,et al.  Vicinity respecting net morphisms , 1991, Applications and Theory of Petri Nets.

[5]  Marek A. Bednarczyk,et al.  General morphisms of Petri nets , 1999 .

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

[7]  C. A. Petri Introduction to General Net Theory , 1979, Advanced Course: Net Theory and Applications.

[8]  Marek A. Bednarczyk,et al.  General Morphisms of Petri Nets (Extended Abstract) , 1999, ICALP.

[9]  Boleslaw Mikolajczak A Parallel Algorithm for Computing all Homomorphisms of Deterministic Finite Automata , 1994, Parallel Processing of Discrete Optimization Problems.

[10]  Rainer Fehling,et al.  A Concept of Hierarchical Petri Nets with Building Blocks , 1991, Applications and Theory of Petri Nets.

[11]  Raymond R. Devillers,et al.  General Refinement for High Level Petri Nets , 1997, FSTTCS.

[12]  Rüdiger Valk,et al.  Petri nets for systems engineering - a guide to modeling, verification, and applications , 2010 .