H. Kong, E. Bartocci, S. Bogomolov, R. Grosu, T. Henzinger, Y. Jiang, C. Schilling:

"Discrete Abstraction of Multiaffine Systems";

Talk: Hybrid Systems Biology - 5th International Workshop, HSB 2016, Grenoble, France, October 20-21, 2016, Proceedings, Grenoble, France; 2016-10-20 - 2016-10-21; in: "Hybrid Systems Biology - 5th International Workshop, HSB 2016, Grenoble, France, October 20-21, 2016, Proceedings", Springer International Publishing, 9957 (2016), ISBN: 978-3-319-47151-8; 128 - 144.

Many biological systems can be modeled as multiaffine hybrid systems. Due to the nonlinearity of multiaffine systems, it is difficult to verify their properties of interest directly. A common strategy to tackle this problem is to construct and analyze a discrete overapproximation of the original system. However, the conservativeness of a discrete abstraction significantly determines the level of confidence we can have in the properties of the original system. In this paper, in order to reduce the conservativeness of a discrete abstraction, we propose a new method based on a sufficient and necessary decision condition for computing discrete transitions between states in the abstract system. We assume the state space partition of a multiaffine system to be based on a set of multivariate polynomials. Hence, a rectangular partition defined in terms of polynomials of the form (xi−c) is just a simple case of multivariate polynomial partition, and the new decision condition applies naturally. We analyze and demonstrate the improvement of our method over the existing methods using some examples.

http://dx.doi.org/10.1007/978-3-319-47151-8_9

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