In our previous work we have introduced the logic STL*, an extension of Signal Temporal Logic (STL) that allows value freezing. In this paper, we define robustness measures for STL* by adapting the robustness measures previously introduced for Metric Temporal Logic (MTL). Furthermore, we present an algorithm for STL* robustness computation, which is implemented in the tool Parasim. Application of STL* robustness analysis is demonstrated on case studies

a b s t r a c tStudies of cells in silico can greatly reduce the need for expensive and prolonged laboratory experimentation. The use of model checking for the analysis of biological networks has attracted much attention recently. The practical limitations are still the size of the model, and the time needed to generate the state space. This paper is focused on the model checking approach for analysis of piecewise-linear deterministic models of genetic regulatory networks. Firstly, the qualitative simulation algorithm of de Jong et al. that builds the heart of Genetic Network Analyzer (GNA) is revisited and its time complexity is studied in detail. Secondly, a novel algorithm that reduces the state space generation time is introduced. The new algorithm is developed as an abstraction of the original GNA algorithm. Finally, a fragment of linear time temporal logic for which the provided abstraction is conservative is identified. Efficiency of the new algorithm when implemented in the parallel model checking environment is demonstrated on a set of experiments performed on randomly modified biological models. In general, the achieved results bring a new insight into the field of qualitative simulation emerging in the context of systems biology.

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In this paper a novel tool BioDiVinE for parallel analysis of biological models is presented. The tool allows analysis of biological models specified in terms of a set of chemical reactions. Chemical reactions are transformed into a system of multi-affine differential equations. BioDiVinE employs techniques for finite discrete abstraction of the continuous state space. At that level, parallel analysis algorithms based on model checking are provided. In the paper, the key tool features are described and their application is demonstrated by means of a case study.

In this paper, a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect the imposed level of approximation provided that with increasing parameter value the approximation converges to the original continuous system. By employing this approximation technique, we present algorithms solving the reachability problem for biochemical dynamical systems. The presented method and algorithms are evaluated on several exemplary biological models and on a real case study