Discrete abstraction of multiaffine systems

Kong, Hui and Bartocci, Ezio and Bogomolov, Sergiy and Grosu, Radu and Henzinger, Thomas A and Jiang, Yu and Schilling, Christian (2016) Discrete abstraction of multiaffine systems. In: HSB: Hybrid Systems Biology, October 20 - 21, 2016, Grenoble, France.

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


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.

Item Type: Conference or Workshop Item (Paper)
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-47151-8_9
Uncontrolled Keywords: Hybrid system; discrete abstraction; Gröbner basis; multiaffine system; state space partition
Subjects: 000 Computer science, knowledge & general works > 000 Computer science, knowledge & systems > 005 Computer programming, programs & data
Research Group: Henzinger Group
SWORD Depositor: Sword Import User
Depositing User: Sword Import User
Date Deposited: 03 Mar 2017 07:11
Last Modified: 17 Oct 2017 07:19
URI: https://repository.ist.ac.at/id/eprint/781

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