2014
DOI: 10.1007/978-3-319-08019-2_20
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Abstract: International audienceWe investigate the computational complexity of deciding the occurrence of many different dynamical behaviours in reaction systems, with an emphasis on biologically relevant problems (i.e., existence of fixed points and fixed point attractors). We show that the decision problems of recognising these dynamical behaviours span a number of complexity classes ranging from FO-uniform AC^0 to Π_2^P-completeness with several intermediate problems being either NP or coNP-complete

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Cited by 26 publications
(31 citation statements)
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“…On one hand, this is surprising because checking them in quantitative frameworks such as ODE-based reaction models or Petri-net models is in general easy and reduces to problems of linear algebra. On the other hand, our results are in line with [6,7] who show that checking properties such as fixed points, cycles, and attractors are also difficult problems for reaction systems. Moreover, our conclusions are in line with the recent results of [11] that introduce a temporal logic for reaction systems and show that model checking in this logic is PSPACEcomplete.…”
Section: Resultssupporting
confidence: 78%
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“…On one hand, this is surprising because checking them in quantitative frameworks such as ODE-based reaction models or Petri-net models is in general easy and reduces to problems of linear algebra. On the other hand, our results are in line with [6,7] who show that checking properties such as fixed points, cycles, and attractors are also difficult problems for reaction systems. Moreover, our conclusions are in line with the recent results of [11] that introduce a temporal logic for reaction systems and show that model checking in this logic is PSPACEcomplete.…”
Section: Resultssupporting
confidence: 78%
“…As shown in [7,Corollary 1], deciding whether a state M is a steady state of a reaction system A is in FO and therefore can be done in polynomial time. The following theorem is an adaptation of [7,Theorem 2], and shows that deciding whether there exists a non-trivial steady state in a reaction system is an NPcomplete problem.…”
Section: Steady States and Elementary Fluxesmentioning
confidence: 99%
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“…It is further assumed that there is a universal set of elements that can enter the system from the outside environment and interact with the reactants at any given time. Several studies have addressed the question of the dynamics of the system (the step by step changes of the states of the system), such as reachability [5], convergence [9], fixed points and cycles [7,8]. It has been observed that the complexity of deciding existence of certain dynamical properties falls within PSPACE (reachability) or NP-completness (fixed points and fixed point attractors).…”
Section: Introductionmentioning
confidence: 99%