Composition Colored Petri Nets for the Refinement of Reaction-based Models

Abstract Model refinement is an important step in the model building process. For reaction-based models, data refinement consists in replacing one species with several of its variants in the refined model. We discuss in this paper the implementation of data refinement with Petri nets such that the size of the model (in terms of number of places and transitions) does not increase. We capture the compositional structure of species by introducing a new class of Petri nets, composition Petri nets (ComP-nets), and their colored counterpart, colored composition Petri nets (ComCP-nets). Given a reaction-based model with known compositional structure, represented as a ComP-net, we propose an algorithm for building a ComCP-net which implements the data refinement of the model and has the same network structure as the initial ComP-net.

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

[2]  Russell Harmer,et al.  Rule-based Modelling and Tunable Resolution , 2009, DCM.

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

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

[5]  Kurt Jensen,et al.  Coloured Petri Nets: Modelling and Validation of Concurrent Systems , 2009 .

[6]  J. van Leeuwen,et al.  Multiset Processing , 2001, Lecture Notes in Computer Science.

[7]  Wolfgang Reisig,et al.  Modeling in Systems Biology, The Petri Net Approach , 2010, Computational Biology.

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

[9]  Wolfgang Reisig,et al.  Understanding Petri nets , 1995, IEEE Parallel & Distributed Technology: Systems & Applications.

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

[11]  Martin Schwarick,et al.  Snoopy - A Unifying Petri Net Tool , 2012, Petri Nets.

[12]  Ion Petre,et al.  Quantitative Model Refinement in Four Different Frameworks, with Applications to the Heat Shock Response , 2016, From Action Systems to Distributed Systems.

[13]  Hassane Alla,et al.  Discrete, continuous, and hybrid Petri Nets , 2004 .

[14]  Ion Petre,et al.  Full structural model refinement as type refinement of colored Petri nets , 2015, BioPPN@Petri Nets.

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

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

[17]  Doktor der Naturwissenschaften.  Colored Petri Nets for Systems Biology , 2012 .

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

[19]  Robert Valette,et al.  Analysis of Petri Nets by Stepwise Refinements , 1979, J. Comput. Syst. Sci..