A. Alfonsi, E. Cancès, G. Turinici, B. Di-ventura, and W. Huisinga, Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems, ESAIM: Proceedings, vol.14, pp.1-13, 2005.
DOI : 10.1051/proc:2005001

URL : https://hal.archives-ouvertes.fr/hal-00536559

R. Alur, T. A. Henzinger, G. Lafferriere, and G. J. Pappas, Discrete abstractions of hybrid systems, Proceedings of the IEEE, vol.88, issue.7, pp.971-984, 2000.
DOI : 10.1109/5.871304

K. R. Apt, Principles of Constraint Programming, 2003.
DOI : 10.1017/CBO9780511615320

M. R. Birtwistle, M. Hatakeyama, N. Yumoto, B. A. Ogunnaike, J. B. Hoek et al., Ligand-dependent responses of the ErbB signaling network: experimental and modeling analyses, Molecular Systems Biology, vol.276, issue.144, 2007.
DOI : 10.1038/msb4100188

A. Bockmayr and A. Courtois, Using Hybrid Concurrent Constraint Programming to Model Dynamic Biological Systems, Proceedings of ICLP'02, International Conference on Logic Programming, pp.85-99, 2002.
DOI : 10.1007/3-540-45619-8_7

URL : https://hal.archives-ouvertes.fr/inria-00107635

H. Bodlaender, Classes of graphs with bounded tree-width, Bulletin of EATCS, pp.116-128, 1988.

M. C. Browne, E. M. Clarke, and O. Grumberg, Characterizing finite Kripke structures in propositional temporal logic, Theoretical Computer Science, vol.59, issue.1-2, pp.115-131, 1988.
DOI : 10.1016/0304-3975(88)90098-9

L. Calzone, F. Fages, and S. Soliman, BIOCHAM: an environment for modeling biological systems and formalizing experimental knowledge, Bioinformatics, vol.22, issue.14, pp.1805-1807, 2006.
DOI : 10.1093/bioinformatics/btl172

URL : https://hal.archives-ouvertes.fr/hal-01431364

L. Calzone, A. Gelay, A. Zinovyev, F. Radvanyi, and E. Barillot, A comprehensive modular map of molecular interactions in RB/E2F pathway, Molecular Systems Biology, vol.4, issue.173, 2008.
DOI : 10.1016/S0092-8674(00)80625-X

F. Centler, C. Kaleta, P. S. Di-fenizio, and P. Dittrich, Computing chemical organizations in biological networks, Bioinformatics, vol.24, issue.14, pp.1611-1618, 2008.
DOI : 10.1093/bioinformatics/btn228

N. Chabrier and F. Fages, Symbolic model checking of biological systems, Poster proceedings of European Conference on Computational Biology ECCB'02, 2002.

N. Chabrier and F. Fages, Symbolic Model Checking of Biochemical Networks, CMSB'03: Proceedings of the first workshop on Computational Methods in Systems Biology, pp.149-162, 2003.
DOI : 10.1007/3-540-36481-1_13

N. Chabrier-rivier, M. Chiaverini, V. Danos, F. Fages, and V. Schächter, Modeling and querying biomolecular interaction networks, Theoretical Computer Science, vol.325, issue.1, pp.25-44, 2004.
DOI : 10.1016/j.tcs.2004.03.063

URL : http://doi.org/10.1016/j.tcs.2004.03.063

F. Chu and X. Xie, Deadlock analysis of petri nets using siphons and mathematical programming, IEEE Transactions on Robotics and Automation, vol.13, issue.6, pp.793-804, 1997.

G. Ciardo, G. Mecham, E. Paviot-adet, and M. Wan, P-Semiflow Computation with Decision Diagrams, PETRI NETS '09: Proceedings of the 30th International Conference on Applications and Theory of Petri Nets, pp.143-162, 2009.
DOI : 10.1007/3-540-58152-9_23

URL : https://hal.archives-ouvertes.fr/hal-01298264

E. M. Clarke, O. Grumberg, and D. A. , Peled. Model Checking, 1999.

J. M. Colom and M. Silva, Convex geometry and semiflows in P/T nets. A comparative study of algorithms for computation of minimal p-semiflows, Proceedings of the 10th International Conference on Application and Theory of Petri Nets, pp.74-95, 1989.
DOI : 10.1007/3-540-53863-1_22

F. Corblin, S. Tripodi, E. Fanchon, D. Ropers, and L. Trilling, A declarative constraint-based method for analyzing discrete genetic regulatory networks, Biosystems, vol.98, issue.2, pp.91-104, 2009.
DOI : 10.1016/j.biosystems.2009.07.007

URL : https://hal.archives-ouvertes.fr/hal-00793012

R. Cordone, L. Ferrarini, and L. Piroddi, Characterization of minimal and basis siphons with predicate logic and binary programming, Proceedings. IEEE International Symposium on Computer Aided Control System Design, pp.193-198, 2002.
DOI : 10.1109/CACSD.2002.1036952

R. Cordone, L. Ferrarini, and L. Piroddi, Some results on the computation of minimal siphons in Petri nets, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2003.
DOI : 10.1109/CDC.2003.1271733

]. R. Cordone, L. Ferrarini, and L. Piroddi, Enumeration Algorithms for Minimal Siphons in Petri Nets Based on Place Constraints, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, vol.35, issue.6, pp.844-854, 2005.
DOI : 10.1109/TSMCA.2005.853504

B. Courcelle, The monadic second-order logic of graphs i. recognizable sets of finite graphs. Information and Computation, pp.12-75, 1990.

P. Cousot and R. Cousot, Abstract interpretation, Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '77, pp.238-252, 1977.
DOI : 10.1145/512950.512973

URL : https://hal.archives-ouvertes.fr/inria-00528590

J. M. Crawford and L. D. Auton, Experimental results on the crossover point in satisfiability problems, Proceedings of the 11th National Conference on Artificial Intelligence, pp.21-27, 1993.

L. F. De-figueiredo, A. Podhorski, A. Rubio, C. Kaleta, J. E. Beasley et al., Computing the shortest elementary flux modes in genome-scale metabolic networks, Bioinformatics, vol.25, issue.23, pp.253158-3165, 2009.
DOI : 10.1093/bioinformatics/btp564

V. Devloo, P. Hansen, and M. Labbe, Identification of all steady states in large networks by logical analysis, Bulletin of Mathematical Biology, vol.65, issue.6, pp.1025-1051, 2003.
DOI : 10.1016/S0092-8240(03)00061-2

URL : https://hal.archives-ouvertes.fr/hal-01255591

D. Diaz and P. Codognet, Design and implementation of the GNU Prolog system, Journal of Functional and Logic Programming, vol.6, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00693240

P. Dittrich and P. Di-fenizio, Chemical Organisation Theory, Bulletin of Mathematical Biology, vol.96, issue.25, pp.1199-1231, 2007.
DOI : 10.1007/s11538-006-9130-8

A. Doi, S. Fujita, H. Matsuno, M. Nagasaki, and S. Miyano, Construction biological pathway models with hybrid functional petri nets, In Silico Biology, vol.4, pp.271-291, 2004.

N. Dudani, S. Ray, S. George, and U. Bhalla, Multiscale modeling and interoperability in MOOSE, BMC Neuroscience, vol.10, issue.Suppl 1, p.54, 2009.
DOI : 10.1186/1471-2202-10-S1-P54

S. Eker, M. Knapp, K. Laderoute, P. Lincoln, J. Meseguer et al., PATHWAY LOGIC: SYMBOLIC ANALYSIS OF BIOLOGICAL SIGNALING, Biocomputing 2002, pp.400-412, 2002.
DOI : 10.1142/9789812799623_0038

F. Fages and S. Soliman, Abstract interpretation and types for systems biology, Theoretical Computer Science, vol.403, issue.1, pp.52-70, 2008.
DOI : 10.1016/j.tcs.2008.04.024

URL : https://hal.archives-ouvertes.fr/hal-01431355

F. Fages, S. Soliman, and N. Chabrier-rivier, Modelling and querying interaction networks in the biochemical abstract machine BIOCHAM, Journal of Biological Physics and Chemistry, vol.4, issue.2, pp.64-73, 2004.
DOI : 10.4024/2040402.jbpc.04.02

URL : https://hal.archives-ouvertes.fr/hal-01431345

F. Fages, S. Soliman, and R. Coolen, CLPGUI: A Generic Graphical User Interface for Constraint Logic Programming, Constraints, vol.9, issue.4, pp.241-262, 2004.
DOI : 10.1023/B:CONS.0000049203.53383.c1

URL : https://hal.archives-ouvertes.fr/hal-01431350

E. Fanchon, F. Corblin, L. Trilling, B. Hermant, and D. Gulino, Modeling the Molecular Network Controlling Adhesion Between Human Endothelial Cells: Inference and Simulation Using Constraint Logic Programming, CMSB'04: Proceedings of the 20 international conference on Computational Methods in Systems Biology, pp.104-118, 2004.
DOI : 10.1007/BF02460695

M. Feinberg, Mathematical aspects of mass action kinetics, Chemical Reactor Theory: A Review, pp.1-78, 1977.

E. C. Freuder, Eliminating interchangeable values in constraint satisfaction problems, Proceedings of AAAI'91, pp.227-233, 1991.

D. Gilbert, M. Heiner, and S. Lehrack, A Unifying Framework for Modelling and Analysing Biochemical Pathways Using Petri Nets, CMSB'07: Proceedings of the fifth international conference on Computational Methods in Systems Biology, 2007.
DOI : 10.1007/978-3-540-75140-3_14

D. T. Gillespie, Exact stochastic simulation of coupled chemical reactions, The Journal of Physical Chemistry, vol.81, issue.25, pp.2340-2361, 1977.
DOI : 10.1021/j100540a008

P. Goss and J. Peccoud, Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets, Proceedings of the National Academy of the United States of America, pp.6750-6755, 1998.
DOI : 10.1073/pnas.95.12.6750

G. Gottlob, N. Leone, and F. Scarcello, A comparison of structural CSP decomposition methods, Artificial Intelligence, vol.124, issue.2, 2000.
DOI : 10.1016/S0004-3702(00)00078-3

R. Goud, K. Van-hee, R. Post, and J. Van-der-werf, Petriweb: A Repository for Petri Nets, Petri Nets and Other Models of Concurrency -ICATPN 2006, pp.411-420, 2006.
DOI : 10.1007/11767589_24

S. Grunwalda, A. Speera, J. Ackermanna, and I. Kocha, Petri net modelling of gene regulation of the Duchenne muscular dystrophy, Biosystems, vol.92, issue.2, pp.189-205, 2008.
DOI : 10.1016/j.biosystems.2008.02.005

M. Heiner, D. Gilbert, and R. Donaldson, Petri Nets for Systems and Synthetic Biology, 8th Int. School on Formal Methods for the Design of Computer, Communication and Software Systems: Computational Systems Biology SFM'08, pp.215-264, 2008.
DOI : 10.1007/978-3-540-68894-5_7

M. Heiner, C. Mahulea, and M. Silva, On the importance of the deadlock trap property for monotonic liveness A satellite event of Petri Nets, Int. Workshop on Biological Processes and Petri Nets (BioPPN), 2010.

S. Helfert, A. Estevez, B. Bakker, P. Michels, and C. Clayton, Roles of triosephosphate isomerase and aerobic metabolism in Trypanosoma brucei, Biochemical Journal, vol.357, issue.1, pp.117-125, 2001.
DOI : 10.1042/bj3570117

R. Hofestädt, A petri net application to model metabolic processes. Systems Analysis Modelling Simulation, pp.113-122, 1994.

R. Hofestädt and S. Thelen, Quantitative modeling of biochemical networks, In In Silico Biology, vol.1, pp.39-53, 1998.

S. Hoops, S. Sahle, R. Gauges, C. Lee, J. Pahle et al., COPASI--a COmplex PAthway SImulator, Bioinformatics, vol.22, issue.24, pp.223067-3074, 2006.
DOI : 10.1093/bioinformatics/btl485

C. Huang, J. E. Ferrell, and J. , Ultrasensitivity in the mitogen-activated protein kinase cascade., Proceedings of the National Academy of Sciences, vol.93, issue.19, pp.10078-10083, 1996.
DOI : 10.1073/pnas.93.19.10078

M. Hucka, The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models, Bioinformatics, vol.19, issue.4, pp.524-531, 2003.
DOI : 10.1093/bioinformatics/btg015

K. Jensen, Coloured Petri Nets and the Invariant-Method, DAIMI Report Series, vol.8, issue.104, pp.317-336, 1981.
DOI : 10.7146/dpb.v8i104.6519

K. Jensen, L. M. Kristensen, and L. Wells, Coloured Petri Nets and CPN Tools for modelling and validation of concurrent systems, International Journal on Software Tools for Technology Transfer, vol.2, issue.2, pp.213-254, 2007.
DOI : 10.1007/s10009-007-0038-x

C. Kaleta, S. Richter, and P. Dittrich, Using chemical organization theory for model checking, Bioinformatics, vol.25, issue.15, pp.1915-1922, 2009.
DOI : 10.1093/bioinformatics/btp332

URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2712341

M. Kinuyama and T. Murata, Generating siphons and traps by petri net representation of logic equations, Proceedings of 2th Conference of the Net Theory SIG-IECE, pp.93-100, 1986.

H. Kitano, Systems Biology: A Brief Overview, Science, vol.295, issue.5560, pp.2951662-1664, 2002.
DOI : 10.1126/science.1069492

I. Koch, B. Junker, and M. Heiner, Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber, Bioinformatics, vol.21, issue.7, pp.1219-1226, 2005.
DOI : 10.1093/bioinformatics/bti145

K. W. Kohn, Molecular Interaction Map of the Mammalian Cell Cycle Control and DNA Repair Systems, Molecular Biology of the Cell, vol.10, issue.8, pp.2703-2734, 1999.
DOI : 10.1091/mbc.10.8.2703

E. Korach and N. Solel, Tree-width, path-width, and cutwidth, Discrete Applied Mathematics, vol.43, issue.1, pp.97-101, 1993.
DOI : 10.1016/0166-218X(93)90171-J

A. Larhlimi and A. Bockmayr, A new constraint-based description of the steady-state flux cone of metabolic networks, Discrete Applied Mathematics, vol.157, issue.10, pp.2257-2266, 2009.
DOI : 10.1016/j.dam.2008.06.039

K. Lautenbach, Linear Algebraic Calculation of Deadlocks and Traps, Concurrency and Nets Advances in Petri Nets, pp.315-336, 1987.
DOI : 10.1007/978-3-642-72822-8_21

C. F. Law, B. H. Gwee, and J. Chang, Fast and memory-efficient invariant computation of ordinary Petri nets, IEE Proceedings: Computers and Digital Techniques, pp.612-624, 2007.
DOI : 10.1049/iet-cdt:20060071

N. Le-novère, B. Bornstein, A. Broicher, M. Courtot, M. Donizelli et al., BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems, Nucleic Acids Research, vol.34, issue.90001, pp.689-691, 2006.
DOI : 10.1093/nar/gkj092

A. Levchenko, J. Bruck, and P. W. Sternberg, Scaffold proteins may biphasically affect the levels of mitogen-activated protein kinase signaling and reduce its threshold properties, Proceedings of the National Academy of Sciences, vol.97, issue.11, pp.975818-5823, 2000.
DOI : 10.1073/pnas.97.11.5818

R. J. Lipton, The reachability problem requires exponential space, 1976.

F. Liu and M. Heiner, Colored petri nets to model and simulate biological systems, ACSD/Petri Nets Workshops 2010, pp.71-85, 2010.

J. Martinez and M. Silva, A simple and fast algorithm to obtain all invariants of a generalized petri net, Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets, pp.301-310, 1982.

W. Marwan, A. Sujatha, and C. Starostzik, Reconstructing the regulatory network controlling commitment and sporulation in Physarum polycephalum based on hierarchical Petri Net modelling and simulation, Journal of Theoretical Biology, vol.236, issue.4, pp.349-365, 2005.
DOI : 10.1016/j.jtbi.2005.03.018

H. Matsuno, A. Doi, M. Nagasaki, and S. Miyano, HYBRID PETRI NET REPRESENTATION OF GENE REGULATORY NETWORK, Biocomputing 2000, pp.338-349, 2000.
DOI : 10.1142/9789814447331_0032

H. Matsuno, Y. Tanaka, H. Aoshima, A. Doi, M. Matsui et al., Biopathways representation and simulation on hybrid functional petri net, In Silico Biology, vol.3, p.32, 2003.

E. W. Mayr, M. Minoux, and K. Barkaoui, An algorithm for the general petri net reachability problem Deadlocks and traps in petri nets as hornsatisfiability solutions and some related polynomially solvable problems, SIAM Journal of Computing Discrete Applied Mathematics, vol.13, issue.29, pp.195-210, 1984.

D. Mitchell, B. Selman, and H. Levesque, Hard and easy distributions of sat problems, Proceedings of the 10th National Conference on Artificial Intelligence, pp.459-465, 1992.

I. Mura and A. Csiksz-nasy, Stochastic Petri Net extension of a yeast cell cycle model, Journal of Theoretical Biology, vol.254, issue.4, pp.850-860, 2008.
DOI : 10.1016/j.jtbi.2008.07.019

T. Murata, Petri nets: Properties, analysis and applications, Proceedings of the IEEE, pp.541-579, 1989.
DOI : 10.1109/5.24143

F. Nabli, Finding minimal siphons as a csp, CP'11: The Seventeenth International Conference on Principles and Practice of Constraint Programming, Doctoral Program, pp.67-72, 2011.

F. Nabli, T. Martinez, F. Fages, and S. Soliman, Finding siphons in petri-nets: Complexity and algorithms (in preparation), Constraints, 2013.

O. Oanea, H. Wimmel, and K. Wolf, New algorithms for deciding the siphontrap property, PETRI NETS'10 Proceedings of the 31st international conference on Applications and Theory of Petri Nets, pp.267-286, 2010.

K. Oda, Y. Matsuoka, A. Funahashi, and H. Kitano, A comprehensive pathway map of epidermal growth factor receptor signaling, Molecular Systems Biology, vol.273, issue.1, 2005.
DOI : 10.1038/msb4100014

J. L. Peterson, Petri Net Theory and the Modeling of Systems, 1981.

A. Pnueli, The temporal logic of programs, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977), pp.46-57, 1977.
DOI : 10.1109/SFCS.1977.32

V. N. Reddy, M. L. Mavrovouniotis, and M. N. Liebman, Petri net representations in metabolic pathways, Proceedings of the 1st International Conference on Intelligent Systems for Molecular Biology (ISMB), pp.328-336, 1993.

N. Robertson and P. Seymour, Graph minors. II. Algorithmic aspects of tree-width, Journal of Algorithms, vol.7, issue.3, pp.309-322, 1986.
DOI : 10.1016/0196-6774(86)90023-4

URL : http://doi.org/10.1006/jctb.1999.1919

A. Sackmann, D. Formanowicz, P. Formanowicz, I. Koch, and J. Blazewicz, An analysis of the Petri net based model of the human body iron homeostasis process, Computational Biology and Chemistry, vol.31, issue.1, pp.1-10, 2007.
DOI : 10.1016/j.compbiolchem.2006.09.005

A. Sackmann, M. Heiner, and I. Koch, Application of petri net based analysis techniques to signal transduction pathways, BMC Bioinformatics, vol.7, issue.482, 2006.

M. A. Savageau, Biochemical systems analysis, Journal of Theoretical Biology, vol.25, issue.3, pp.365-369, 1969.
DOI : 10.1016/S0022-5193(69)80026-3

M. A. Savageau, Biochemical systems analysis, Journal of Theoretical Biology, vol.25, issue.3, pp.370-379, 1969.
DOI : 10.1016/S0022-5193(69)80027-5

B. Schoeberl, C. Eichler-jonsson, E. Gilles, and G. Muller, Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors, Nature Biotechnology, vol.20, issue.4, pp.370-375, 2002.
DOI : 10.1038/nbt0402-370

S. Soliman, Finding minimal P/T-invariants as a CSP, Proceedings of the fourth Workshop on Constraint Based Methods for Bioinformatics WCB'08, 2008.

S. Soliman, Modelling biochemical reaction networks with biocham extracting qualitative and quantitative information from the structure, Proceedings of the 6th Vienna Conference on Mathematical Modelling MATHMOD'09, pp.2304-2312, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00419776

S. Soliman, Invariants and Other Structural Properties of Biochemical Models as a Constraint Satisfaction Problem, Algorithms for Molecular Biology, vol.7, issue.1, 2012.
DOI : 10.1007/BF01211911

URL : https://hal.archives-ouvertes.fr/hal-00784404

N. Soranzo and C. Altafini, ERNEST: a toolbox for chemical reaction network theory, Bioinformatics, vol.25, issue.21, pp.2853-2854, 2009.
DOI : 10.1093/bioinformatics/btp513

R. Srivastava, M. Peterson, and W. Bentley, Stochastic kinetic analysis of theEscherichia coli stress circuit using ?32-targeted antisense, Biotechnology and Bioengineering, vol.47, issue.1, pp.120-129, 2001.
DOI : 10.1002/bit.1171

L. J. Steggles, R. Banks, and A. Wipat, Modelling and Analysing Genetic Networks: From Boolean Networks to Petri Nets, CMSB06, pp.127-141, 2006.
DOI : 10.1007/11885191_9

Z. Szallasi, J. Stelling, and V. Periwal, System Modeling in Cellular Biology: From Concepts to Nuts and Bolts, 2006.
DOI : 10.7551/mitpress/9780262195485.001.0001

S. Tanimoto, M. Yamauchi, and T. Watanabe, Finding minimal siphons in general petri nets Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and Molecular Biologists, IEICE Trans. on Fundamentals in Electronics Communications and Computer Science, pp.1817-1824, 1996.

A. Kamp and S. Schuster, Metatool 5.0: fast and flexible elementary modes analysis, Bioinformatics, vol.22, issue.15, pp.1930-1931, 2006.
DOI : 10.1093/bioinformatics/btl267

M. Wallace, Practical applications of constraint programming, Constraints, vol.16, issue.3, pp.139-168, 1996.
DOI : 10.1007/BF00143881

M. Yamauchi, M. Wakuda, S. Taoka, and T. Watanabe, A fast and spacesaving algorithm for computing invariants of petri nets, Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics IEEE SMC '99, pp.866-871, 1999.

M. Yamauchi and T. Watanabe, Time complexity analysis of the minimal siphon extraction problem of petri nets, EICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences, pp.2558-2565, 1999.

I. Zevedei-oancea and S. Schuster, Topological analysis of metabolic networks based on petri net theory, In Silico Biology, vol.3, issue.29, 2003.