# Analyzing the dynamics of deterministic systems from a hypergraph theoretical point of view

Luis M. Torres; Annegret K. Wagler

RAIRO - Operations Research - Recherche Opérationnelle (2013)

- Volume: 47, Issue: 3, page 321-330
- ISSN: 0399-0559

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topTorres, Luis M., and Wagler, Annegret K.. "Analyzing the dynamics of deterministic systems from a hypergraph theoretical point of view." RAIRO - Operations Research - Recherche Opérationnelle 47.3 (2013): 321-330. <http://eudml.org/doc/275007>.

@article{Torres2013,

abstract = {To model the dynamics of discrete deterministic systems, we extend the Petri nets framework by a priority relation between conflicting transitions, which is encoded by orienting the edges of a transition conflict graph. The aim of this paper is to gain some insight into the structure of this conflict graph and to characterize a class of suitable orientations by an analysis in the context of hypergraph theory.},

author = {Torres, Luis M., Wagler, Annegret K.},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {Petri nets; deterministic dynamic systems; hypergraphs},

language = {eng},

number = {3},

pages = {321-330},

publisher = {EDP-Sciences},

title = {Analyzing the dynamics of deterministic systems from a hypergraph theoretical point of view},

url = {http://eudml.org/doc/275007},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Torres, Luis M.

AU - Wagler, Annegret K.

TI - Analyzing the dynamics of deterministic systems from a hypergraph theoretical point of view

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 3

SP - 321

EP - 330

AB - To model the dynamics of discrete deterministic systems, we extend the Petri nets framework by a priority relation between conflicting transitions, which is encoded by orienting the edges of a transition conflict graph. The aim of this paper is to gain some insight into the structure of this conflict graph and to characterize a class of suitable orientations by an analysis in the context of hypergraph theory.

LA - eng

KW - Petri nets; deterministic dynamic systems; hypergraphs

UR - http://eudml.org/doc/275007

ER -

## References

top- [1] B.D. Acharya and M. Las Vergnas, Hypergraphs with cyclomatic number zero, triangulated hypergraphs and an inequality. J. Combin. Theory (B) 33 (1982) 52–56. Zbl0506.05047MR678170
- [2] N.R. Adam, V. Atluri and W.K. Huang, Modeling and analysis of workflows using Petri nets. J. Intell. Inf. Syst.10 (1998) 131–158.
- [3] G. Balbo, Introducation to stochastic Petri nets, in Lectures on formal methods and performance analysis: first EEF/Euro summer school on trends in computer science, Springer-Verlag New York, Inc., New York, NY, USA (2002) 84–155. Zbl0990.68092MR1916976
- [4] C. Berge and P. Duchet, A generalisation of Gilmore’s theorem, in Recent advances in graph theory, edited by M. Fiedler, Acad. Praha, Prague (1975) 49–55. Zbl0325.05125MR406801
- [5] J. Billington, M. Diaz and G. Rozenberg, Application of Petri nets to communication networks, Advances in Petri Nets. Springer-Verlag, London, UK (1999)
- [6] R. David and H. Alla, Discrete, Continuous, and hybrid Petri nets. Springer-Verlag Berlin Heidelberg, Heidelberg (2005). Zbl1074.93002MR2104104
- [7] P. Duchet, Propriété de helly et problèmes de représentations, in Problèmes Combinatoires et Théorie des Graphes, Coll. Orsay 1976, CNRS Paris (1978) 117–118. Zbl0413.05042
- [8] C. Flament, Hypergraphes arborés. Discrete Math.21 (1978) 223–226. Zbl0393.05039MR522896
- [9] T. Gu and P.A. Bahri, A survey of Petri net applications in batch processes. Comput. Ind.47 (2002) 99–111.
- [10] S. Hardy and P.N. Robillard, Modeling and simulation of molecular biology systems using Petri nets: modeling goals of various approaches. J. Bioinform. Comput. Biol.2 (2004) 619–637.
- [11] K. Jensen, Coloured Petri nets: basic concepts, analysis methods and practical use, vol. 3, Springer-Verlag New York, Inc., New York, NY, USA (1997) Zbl0883.68098
- [12] I. Koch and M. Heiner, Petri nets, in Analysis of biological networks, edited by B.H. Junker and F. Schreiber, Wiley Book Series in Bioinformatics (2008) 139–180.
- [13] M. Marsan, G. Balbo, S. Donatelli, G. Franceschinis and G. Conte, Modelling with generalized stochastic Petri nets. Wiley Series in Parallel Computing (1995). Zbl0843.68080
- [14] W. Marwan, Theory of time-resolved somatic complementation and its use for the analysis of the sporulation control network of Physarum polycephalum. Genetics164 (2003) 105–115.
- [15] W. Marwan and C. Starostzik, The sequence of regulatory events in the sporulation control network of Physarum polycephalum analysed by time-resolved somatic complementation of mutants. Protist153 (2002) 391–400.
- [16] W. Marwan, A. Sujatha and C. Starostzik, Reconstructing the regulatory network controlling commitment and sporulation in Physarum polycephalum based on hierarchical Petri net modeling and simulation. J. Theor. Biol.236 (2005) 349–365.
- [17] W. Marwan, A. Wagler and R. Weismantel, A mathematical approach to solve the network reconstruction problem. Math. Meth. Oper. Res.67 (2008) 117–132. Zbl1146.90016MR2373000
- [18] W. Reisig, Petri nets: an introduction. Springer-Verlag New York, Inc., New York, NY, USA (1985). Zbl0555.68033MR782303
- [19] W. Reisig, Elements of distributed algorithms: modeling and analysis with Petri nets. Springer-Verlag New York, Inc., New York, NY, USA (1998). Zbl0907.68130
- [20] P.J. Slater, A characterization of soft hypergraphs. Canad. Math. Bull.21 (1978) 335–337. Zbl0391.05042MR511582
- [21] L.M. Torres and A. Wagler, Model reconstruction for discrete deterministic systems. Electronic Notes of Discrete Mathematics36 (2010) 175–182. Zbl1237.90212
- [22] L.M. Torres and A. Wagler, Encoding the dynamics of deterministic systems. Math. Methods Operations Res.73 (2011) 281–300. Zbl1228.93079MR2805935
- [23] A. Yakovlev, A. Koelmans, A. Semenov and D. Kinniment, Modelling, analysis and synthesis of asynchronous control circuits using Petri nets. Integr. VLSI J.21 (1996) 143–170. Zbl0875.68972

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