On the complexity of verifying concurrent transition systems
Information and Computation
A survey of basic net models and modular net classes
Advances in Petri Nets 1992, The DEMON Project
Minimal cut sets in biochemical reaction networks
Bioinformatics
Semantics of Biological Regulatory Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
Refining dynamics of gene regulatory networks in a stochastic π-calculus framework
Transactions on computational systems biology XIII
Static analysis of biological regulatory networks dynamics using abstract interpretation
Mathematical Structures in Computer Science
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In the scope of discrete finite-state models of interacting components, we present a novel algorithm for identifying sets of local states of components whose activity is necessary for the reachability of a given local state. If all the local states from such a set are disabled in the model, the concerned reachability is impossible. Those sets are referred to as cut sets and are computed from a particular abstract causality structure, so-called Graph of Local Causality, inspired from previous work and generalised here to finite automata networks. The extracted sets of local states form an under-approximation of the complete minimal cut sets of the dynamics: there may exist smaller or additional cut sets for the given reachability. Applied to qualitative models of biological systems, such cut sets provide potential therapeutic targets that are proven to prevent molecules of interest to become active, up to the correctness of the model. Our new method makes tractable the formal analysis of very large scale networks, as illustrated by the computation of cut sets within a Boolean model of biological pathways interactions gathering more than 9000 components.