Discrete abstraction of multiaffine systems Conference Paper

Author(s): Kong, Hui; Bartocci, Ezio; Bogomolov, Sergiy V; Grosu, Radu; Henzinger, Thomas A; Jiang, Yu; Schilling, Christian
Title: Discrete abstraction of multiaffine systems
Title Series: LNCS
Affiliation IST Austria
Abstract: 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.
Keywords: Hybrid system; Discrete abstraction; Gröbner basis; Multiaffine system; State space partition
Conference Title: HSB: Hybrid Systems Biology
Volume: 9957
Conference Dates: October 20 - 21, 2016
Conference Location: Grenoble, France
ISBN: 978-3-319-26915-3
Publisher: Springer  
Date Published: 2016-09-25
Start Page: 128
End Page: 144
Sponsor: This research was supported in part by the Austrian Science Fund (FWF) under grants S11402-N23, S11405-N23 and S11412-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award).
DOI: 10.1007/978-3-319-47151-8_9
Open access: yes (repository)
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
  2. Hui Kong
    9 Kong
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