Efficient Parallel Statistical Model Checking of Biochemical Networks

We consider the problem of verifying stochastic models of biochemical networks against behavioral properties expressed in temporal logic terms. Exact probabilistic verification approaches such as, for example, CSL/PCTL model checking, are undermined by a huge computational demand which rule them out for most real case studies. Less demanding approaches, such as statistical model checking, estimate the likelihood that a property is satisfied by sampling executions out of the stochastic model. We propose a methodology for efficiently estimating the likelihood that a LTL property P holds of a stochastic model of a biochemical network. As with other statistical verification techniques, the methodology we propose uses a stochastic simulation algorithm for generating execution samples, however there are three key aspects that improve the efficiency: first, the sample generation is driven by on-the-fly verification of P which results in optimal overall simulation time. Second, the confidence interval estimation for the probability of P to hold is based on an efficient variant of the Wilson method which ensures a faster convergence. Third, the whole methodology is designed according to a parallel fashion and a prototype software tool has been implemented that performs the sampling/verification process in parallel over an HPC architecture

Constructive Negation by Pruning

FIXPOINT SEMANTICS 15 5 THREE-VALUED LOGICAL SEMANTICS 21 6 COMPARISON WITH OTHER WORKS 23 7 VARIATIONS ON A SCHEME FOR OPTIMIZATION PREDICATES 25 7.1 Constraint Minimization : : : : : : : : : : : : : : : : : : : : : : : : : 25 7.2 Query Optimization : : : : : : : : : : : : : : : : : : : : : : : : : : : 26 7.3 Global Optimization Predicates : : : : : : : : : : : : : : : : : : : : : 28 7.4 Local Optimization Predicates : : : : : : : : : : : : : : : : : : : : : 31 8 CONCLUSION 32 1. INTRODUCTION Constraint logic programming and concurrent constraint programming are simple and powerful models of computation that have been implemented in several systems over the last decade, and proved successful in a variety of applications ranging from combinatorial optimization problems to complex system modeling [16]. Extending these classes of languages with a negation operator is a major issue as it allows the user to express arbitrary logical combinations of relations. Negation in logic programmi..

The biochemical abstract machine BIOCHAM

Abstract. In this article we present the Biochemical Abstract Machine BIOCHAM and advocate its use as a formal modeling environment for networks biology. Biocham provides a precise semantics to biomolecular interaction maps. Based on this formal semantics, the Biocham system offers automated reasoning tools for querying the temporal properties of the system under all its possible behaviors. We present the main features of Biocham, provide details on a simple example of the MAPK signaling cascade and prove some results on the equivalence of models w.r.t. their temporal properties. 1 Introduction In networks biology, the complexity of the systems at hand (metabolic net-works, extracellular and intracellular networks, networks of gene regulation) clearly shows the necessity of software tools for reasoning globally about bio-logical systems [1]. Several formalisms have been proposed in recent years for modeling biochemical processes either qualitatively [2-4] or quantitatively [5-9].State-of-the-art tools integrate a graphical user interface and a simulator, yet few formal tools are available for reasoning about these processes and provingproperties about them. Our focus in Biocham has been on the design of a biochemical rule language and a query language of the model in temporal logic,that are intended to be used by biologists. Biocham has been designed in the framework of the ARC CPBIO on "ProcessCalculi and Biology of Molecular Networks " [10] which aims at pushing forward a declarative and compositional approach to modeling languages in SystemsBiology. Biocham is a language and a programming environment for modeling biochemical systems, making simulations, and checking temporal properties. Itis composed of