Computation tree regular logic for genetic regulatory networks
R. Mateescu, P.T. Monteiro, E. Dumas and H. de Jong
Technical Report INRIA, RR-6521, 2008
Model checking has proven to be a useful analysis technique not only for concurrent systems, but also for the genetic regulatory networks (GRNs) that govern the functioning of living cells. The applications of model checking in systems biology have revealed that temporal logics should be able to capture both branching-time and fairness properties (needed for specifying multistability and oscillation properties, respectively). At the same time, they should have a user-friendly syntax easy to employ by non-experts. In this report, we deﬁne Computation Tree Regular Logic (CTRL), an extension of CTL with regular expressions and fairness operators that attempts to match these criteria. CTRL subsumes both CTL and LTL, and has a reduced set of temporal operators indexed by regular expressions, inspired from the modalities of Propositional Dynamic Logic (PDL). We also develop a translation of CTRL into Hennessy-Milner Logic with Recursion (HMLR), an equational variant of the modal µ-calculus. This has allowed us to obtain an on-the-ﬂy model checker with diagnostic for CTRL by directly reusing the veriﬁcation technology available in the CADP toolbox. We illustrate the application of the CTRL model checker by analyzing the GRN controlling the carbon starvation response of Escherichia coli.