Efficient Unfolding of Coloured Petri Nets Using Interval Decision Diagrams

We consider coloured Petri nets, qualitative and quantitative ones alike, as supported by our PetriNuts tool family, comprising, among others, Snoopy, Marcie and Spike. Currently, most analysis and simulation techniques require to unfold the given coloured Petri net into its corresponding plain, uncoloured Petri net representation. This unfolding step is rather straightforward for finite discrete colour sets, but tends to be time-consuming due to the potentially huge number of possible transition bindings. We present an unfolding approach building on a special type of symbolic data structures, called Interval Decision Diagram, and compare its runtime performance with an unfolding engine employing an off-the-shelf library to solve constraint satisfaction problems. For this comparison we use the 22 scalable coloured models from the MCC benchmark suite, complemented by a few from our own collection.

[1]  Kurt Lautenbach,et al.  A Completion of the S–invariance Technique by means of Fixed Point Algorithms , 2007 .

[2]  Fabrice Kordon,et al.  Optimized Colored Nets Unfolding , 2006, FORTE.

[3]  Monika Heiner,et al.  A Graphical Approach for Hybrid Modelling of Intracellular Calcium Dynamics Based on Coloured Hybrid Petri Nets , 2019, Automated Reasoning for Systems Biology and Medicine.

[4]  Kurt Lautenbach,et al.  The Analysis of Distributed Systems by Means of Predicate ? Transition-Nets , 1979, Semantics of Concurrent Computation.

[5]  Martin Schwarick,et al.  Hybrid Petri Nets for Modelling the Eukaryotic Cell Cycle , 2013, Trans. Petri Nets Other Model. Concurr..

[6]  Martin Schwarick,et al.  Symbolic on-the-fly analysis of stochastic Petri nets , 2014 .

[7]  Emmanuelle Encrenaz-Tiphène,et al.  Data Decision Diagrams for Petri Net Analysis , 2002, ICATPN.

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

[9]  Fabrice Kordon,et al.  Petri Nets Repository: A Tool to Benchmark and Debug Petri Net Tools , 2017, Petri Nets.

[10]  B. Peña,et al.  Stability of Turing patterns in the Brusselator model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[12]  Martin Schwarick,et al.  MARCIE's Secrets of Efficient Model Checking , 2016, Trans. Petri Nets Other Model. Concurr..

[13]  Martin Schwarick,et al.  IDD-based model validation of biochemical networks , 2011, Theor. Comput. Sci..

[14]  Monika Heiner,et al.  Coloured Hybrid Petri Nets: An adaptable modelling approach for multi-scale biological networks , 2018, Comput. Biol. Chem..

[15]  LiuFei,et al.  Multiscale Modeling and Analysis of Planar Cell Polarity in the Drosophila Wing , 2013 .

[16]  Martin Schwarick,et al.  CSL Model Checking of Biochemical Networks with Interval Decision Diagrams , 2009, CMSB.

[17]  Monika Heiner,et al.  Spatial-Temporal Modelling and Analysis of Bacterial Colonies with Phase Variable Genes , 2015, ACM Trans. Model. Comput. Simul..

[18]  Kurt Jensen,et al.  Coloured Petri Nets and the Invariant-Method , 1981, Theor. Comput. Sci..

[19]  Martin Schwarick,et al.  A comparative study of stochastic analysis techniques , 2010, CMSB '10.

[20]  Emden R. Gansner,et al.  An open graph visualization system and its applications to software engineering , 2000, Softw. Pract. Exp..

[21]  Lothar Thiele,et al.  Symbolic model checking using interval diagram techniques , 1998 .

[22]  Lars Michael Kristensen,et al.  Implementing Coloured Petri Nets Using a Functional Programming Language , 2004, High. Order Symb. Comput..

[23]  Monika Heiner,et al.  Spike - Reproducible Simulation Experiments with Configuration File Branching , 2019, CMSB.

[24]  Marko Mäkelä,et al.  Optimising Enabling Tests and Unfoldings of Algebraic System Nets , 2001, ICATPN.

[25]  Martin Schwarick,et al.  MARCIE - Model Checking and Reachability Analysis Done EffiCIEntly , 2011, 2011 Eighth International Conference on Quantitative Evaluation of SysTems.

[26]  L. Thiele,et al.  Symbolic model checking of process networks using interval diagram techniques , 1998, 1998 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (IEEE Cat. No.98CB36287).

[27]  Ming Yang,et al.  Modelling and simulating reaction-diffusion systems using coloured Petri nets , 2014, Comput. Biol. Medicine.

[28]  Ming Yang,et al.  An efficient method for unfolding colored Petri nets , 2012, Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC).

[29]  Monika Heiner,et al.  Multiscale modelling of coupled Ca2+ channels using coloured stochastic Petri nets. , 2013, IET systems biology.

[30]  Alexey A. Tovchigrechko Efficient symbolic analysis of bounded Petri nets using interval decision diagrams , 2008 .

[31]  Monika Heiner,et al.  Colouring Space - A Coloured Framework for Spatial Modelling in Systems Biology , 2013, Petri Nets.

[32]  Marco Beccuti,et al.  Decision Diagrams for Petri Nets: Which Variable Ordering? , 2017, PNSE @ Petri Nets.

[33]  John D. Hunter,et al.  Matplotlib: A 2D Graphics Environment , 2007, Computing in Science & Engineering.