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.
Keywords: 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},
year = {2013},
publisher = {EDP Sciences},
volume = {47},
number = {3},
doi = {10.1051/ro/2013035},
mrnumber = {3143756},
zbl = {1301.90012},
language = {en},
url = {https://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 - https://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 https://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
[1] and , Hypergraphs with cyclomatic number zero, triangulated hypergraphs and an inequality. J. Combin. Theory (B) 33 (1982) 52-56. | Zbl | MR
[2] , and , Modeling and analysis of workflows using Petri nets. J. Intell. Inf. Syst. 10 (1998) 131-158.
[3] , 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. | Zbl | MR
[4] and , A generalisation of Gilmore's theorem, in Recent advances in graph theory, edited by M. Fiedler, Acad. Praha, Prague (1975) 49-55. | Zbl | MR
[5] , and , Application of Petri nets to communication networks, Advances in Petri Nets. Springer-Verlag, London, UK (1999)
[6] and , Discrete, Continuous, and hybrid Petri nets. Springer-Verlag Berlin Heidelberg, Heidelberg (2005). | Zbl | MR
[7] , Propriété de helly et problèmes de représentations, in Problèmes Combinatoires et Théorie des Graphes, Coll. Orsay 1976, CNRS Paris (1978) 117-118. | Zbl
[8] , Hypergraphes arborés. Discrete Math. 21 (1978) 223-226. | Zbl | MR
[9] and , A survey of Petri net applications in batch processes. Comput. Ind. 47 (2002) 99-111.
[10] and , Modeling and simulation of molecular biology systems using Petri nets: modeling goals of various approaches. J. Bioinform. Comput. Biol. 2 (2004) 619-637.
[11] , Coloured Petri nets: basic concepts, analysis methods and practical use, vol. 3, Springer-Verlag New York, Inc., New York, NY, USA (1997) | Zbl
[12] and , Petri nets, in Analysis of biological networks, edited by B.H. Junker and F. Schreiber, Wiley Book Series in Bioinformatics (2008) 139-180.
[13] , , , and , Modelling with generalized stochastic Petri nets. Wiley Series in Parallel Computing (1995). | Zbl
[14] , 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] and , 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] , and , 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] , and , A mathematical approach to solve the network reconstruction problem. Math. Meth. Oper. Res. 67 (2008) 117-132. | Zbl | MR
[18] , Petri nets: an introduction. Springer-Verlag New York, Inc., New York, NY, USA (1985). | Zbl | MR
[19] , Elements of distributed algorithms: modeling and analysis with Petri nets. Springer-Verlag New York, Inc., New York, NY, USA (1998). | Zbl
[20] , A characterization of soft hypergraphs. Canad. Math. Bull. 21 (1978) 335-337. | Zbl | MR
[21] and , Model reconstruction for discrete deterministic systems. Electronic Notes of Discrete Mathematics 36 (2010) 175-182. | Zbl
[22] and , Encoding the dynamics of deterministic systems. Math. Methods Operations Res. 73 (2011) 281-300. | Zbl | MR
[23] , , and , Modelling, analysis and synthesis of asynchronous control circuits using Petri nets. Integr. VLSI J. 21 (1996) 143-170. | Zbl
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