no. 3
Analyzing the dynamics of deterministic systems from a hypergraph theoretical point of view
RAIRO - Operations Research - Recherche Opérationnelle, Tome 47 (2013) no. 3, pp. 321-330.

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.

DOI : 10.1051/ro/2013035
Classification : 92C42, 68Q85, 05C65
Mots clés : Petri nets, deterministic dynamic systems, hypergraphs 
@article{RO_2013__47_3_321_0,
     author = {Torres, Luis M. and Wagler, Annegret K.},
     title = {Analyzing the dynamics of deterministic systems from a hypergraph theoretical point of view},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {321--330},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {3},
     year = {2013},
     doi = {10.1051/ro/2013035},
     mrnumber = {3143756},
     zbl = {1301.90012},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2013035/}
}
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
SP  - 321
EP  - 330
VL  - 47
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2013035/
DO  - 10.1051/ro/2013035
LA  - en
ID  - RO_2013__47_3_321_0
ER  - 
%0 Journal Article
%A Torres, Luis M.
%A Wagler, Annegret K.
%T Analyzing the dynamics of deterministic systems from a hypergraph theoretical point of view
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2013
%P 321-330
%V 47
%N 3
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2013035/
%R 10.1051/ro/2013035
%G en
%F RO_2013__47_3_321_0
Torres, Luis M.; Wagler, Annegret K. Analyzing the dynamics of deterministic systems from a hypergraph theoretical point of view. RAIRO - Operations Research - Recherche Opérationnelle, Tome 47 (2013) no. 3, pp. 321-330. doi : 10.1051/ro/2013035. http://www.numdam.org/articles/10.1051/ro/2013035/

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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). | MR | Zbl

[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. | Zbl

[8] C. Flament, Hypergraphes arborés. Discrete Math. 21 (1978) 223-226. | MR | Zbl

[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) | Zbl

[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). | Zbl

[14] W. Marwan, Theory of time-resolved somatic complementation and its use for the analysis of the sporulation control network of Physarum polycephalum. Genetics 164 (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. Protist 153 (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. | MR | Zbl

[18] W. Reisig, Petri nets: an introduction. Springer-Verlag New York, Inc., New York, NY, USA (1985). | MR | Zbl

[19] W. Reisig, Elements of distributed algorithms: modeling and analysis with Petri nets. Springer-Verlag New York, Inc., New York, NY, USA (1998). | Zbl

[20] P.J. Slater, A characterization of soft hypergraphs. Canad. Math. Bull. 21 (1978) 335-337. | MR | Zbl

[21] L.M. Torres and A. Wagler, Model reconstruction for discrete deterministic systems. Electronic Notes of Discrete Mathematics 36 (2010) 175-182. | Zbl

[22] L.M. Torres and A. Wagler, Encoding the dynamics of deterministic systems. Math. Methods Operations Res. 73 (2011) 281-300. | MR | Zbl

[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. | Zbl

Cité par Sources :