Abstract.Recently, there has been considerable interest in the use of Model Checking for Systems Biology. Unfortunately, the state space of stochastic biological models is often too large for classical Model Checking techniques. For these models, a statistical approach to Model Checking has been shown to be an effective alternative. Extending our earlier work, we present the first algorithm for performing statistical Model Checking using Bayesian Sequential Hypothesis Testing. We show that our Bayesian approach outperforms current statistical Model Checking techniques, which rely on tests from Classical (aka Frequentist) statistics, by requiring fewer system simulations. Another advantage of our approach is the ability to incorporate prior Biological knowledge about the model being verified. We demonstrate our algorithm on a variety of models from the Systems Biology literature and show that it enables faster verification than state-of-the-art techniques, even when no prior knowledge is available.

Abstract. Our goal is to find the set of parameters for which a given linear hybrid automaton does not reach a given set of bad states. The problem is known to be semi-solvable (if the algorithm terminates the result is correct) by introducing the parameters as state variables and computing the set of reachable states. This is usually too expensive, however, and in our experiments only possible for very simple systems with few parameters. We propose an adaptation of counterexample-guided abstraction refinement (CEGAR) with which one can obtain an underapproximation of the set of good parameters using linear programming. The adaptation is generic and can be applied on top of any CEGAR method where the counterexamples correspond to paths in the concrete system. For each counterexample, the cost incurred by underapproximating the parameters is polynomial in the number of variables, parameters, and the length of counterexample. We identify a syntactic condition for which the approach is complete in the sense that the underapproximation is empty only if the problem has no solution. Experimental results are provided for two CEGAR methods, a simple discrete version and iterative relaxation abstraction (IRA), both of which show a drastic improvement in performance compared to standard reachability.

Abstract. We present an algorithm, called BioLab, for verifying temporal properties of rule-based models of cellular signalling networks. BioLab models are encoded in the BioNetGen language, and properties are expressed as formulae in probabilistic bounded linear temporal logic. Temporal logic is a formalism for representing and reasoning about propositions qualified in terms of time. Properties are then verified using sequential hypothesis testing on executions generated using stochastic simulation. BioLab is optimal, in the sense that it generates the minimum number of executions necessary to verify the given property. BioLab also provides guarantees on the probability of it generating Type-I (i.e., false-positive) and Type-II (i.e., false-negative) errors. Moreover, these error bounds are pre-specified by the user. We demonstrate BioLab by verifying stochastic effects and bistability in the dynamics of the T-cell receptor signaling network.