Full structural model refinement as type refinement of colored Petri nets

In this paper we propose a method for implementing a full structural model refinement of a (biological) model represented as a (colored) Petri net. We build on the full structural data refinement definition of C. Gratie and Petre, and the type refinement of colored Petri nets introduced by Charles Lakos. Given a (biological) reaction-based model and a desired full structural refinement of it, we propose a general coloring scheme for a colored Petri net implementation of the model and give an algorithm for adding the refinement details in the Petri net model. We then prove that the construction is a type refinement, and that by our choice of color sets the resulting refined colored Petri net implements the full structural refinement of the given model.

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

[2]  Vincent Danos,et al.  Rule Based Modeling and Model Refinement , 2010 .

[3]  Ion Petre,et al.  Quantitative Refinement of Reaction Models , 2012, Int. J. Unconv. Comput..

[4]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[5]  Marco Pistore,et al.  A Partition Refinement Algorithm for the pi-Calculus (Extended Abstract) , 1996, CAV.

[6]  René David,et al.  Petri nets for modeling of dynamic systems: A survey , 1994, Autom..

[7]  Ion Petre,et al.  On the Implementation of Quantitative Model Refinement , 2014, AlCoB.

[8]  Ion Petre,et al.  Self-assembly Models of Variable Resolution , 2012, Trans. Comp. Sys. Biology.

[9]  Ralph-Johan Back,et al.  Refinement Calculus: A Systematic Introduction , 1998 .

[10]  Laure Petrucci,et al.  Coloured Petri Nets Refinements , 2013, PNSE+ModPE.

[11]  Vincent Danos,et al.  Rule-Based Modelling and Model Perturbation , 2009, Trans. Comp. Sys. Biology.

[12]  Claudine Chaouiya,et al.  Petri net modelling of biological networks , 2007, Briefings Bioinform..

[13]  Ichiro Suzuki,et al.  A Method for Stepwise Refinement and Abstraction of Petri Nets , 1983, J. Comput. Syst. Sci..

[14]  Kurt Jensen,et al.  Coloured Petri nets: A high level language for system design and analysis , 1991, Applications and Theory of Petri Nets.

[15]  Ion Petre,et al.  Fit-Preserving Data Refinement of Mass-Action Reaction Networks , 2014, CiE.

[16]  Serge Haddad,et al.  Application and Theory of Petri Nets , 2012, Lecture Notes in Computer Science.