NuSMV 2: An OpenSource Tool for Symbolic Model Checking
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
RSP '03 Proceedings of the 14th IEEE International Workshop on Rapid System Prototyping (RSP'03)
Local Structure and Behavior of Boolean Bioregulatory Networks
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
Relating attractors and singular steady states in the logical analysis of bioregulatory networks
AB'07 Proceedings of the 2nd international conference on Algebraic biology
Detecting inconsistencies in large biological networks with answer set programming
Theory and Practice of Logic Programming
Comparing discrete and piecewise affine differential equation models of gene regulatory networks
IPCAT'12 Proceedings of the 9th international conference on Information Processing in Cells and Tissues
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In the field of biological regulation, models extracted from experimental works are usually complex networks comprising intertwined feedback circuits. The overall behavior is difficult to grasp and the development of formal methods is needed in order to model and simulate biological regulatory networks. To model the behavior of such systems, R. Thomas and coworkers developed a qualitative approach in which the dynamics is described by a state transition system. Even if all steady states of the system can be detected in this formalism, some of them, the singular ones, are not formally included in the transition system. Consequently, temporal properties in which singular states have to be described, cannot be checked against the transition system. However, steady singular states play an essential role in the dynamics since they can induce homeostasis or multistationnarity and sometimes are associated to biological phenotypes. These observations motivated our interest for developing an extension of Thomas formalism in which all singular states are represented, allowing us to check temporal properties concerning singular states. We easily demonstrate in our formalism the previously demonstrated theorems giving the conditions for the steadiness of singular states. We also prove that our formalism is coherent with the Thomas one since all paths of the Thomas transition system are preserved in our one, which in addition includes singular states.