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.
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).
128 - 144
HSB: Hybrid Systems Biology
2016-10-20 – 2016-10-21
Kong H, Bartocci E, Bogomolov S, et al. Discrete abstraction of multiaffine systems. In: Vol 9957. Springer; 2016:128-144. doi:10.1007/978-3-319-47151-8_9
Kong, H., Bartocci, E., Bogomolov, S., Grosu, R., Henzinger, T. A., Jiang, Y., & Schilling, C. (2016). Discrete abstraction of multiaffine systems (Vol. 9957, pp. 128–144). Presented at the HSB: Hybrid Systems Biology, Grenoble, France: Springer. https://doi.org/10.1007/978-3-319-47151-8_9
Kong, Hui, Ezio Bartocci, Sergiy Bogomolov, Radu Grosu, Thomas A Henzinger, Yu Jiang, and Christian Schilling. “Discrete Abstraction of Multiaffine Systems,” 9957:128–44. Springer, 2016. https://doi.org/10.1007/978-3-319-47151-8_9.
H. Kong et al., “Discrete abstraction of multiaffine systems,” presented at the HSB: Hybrid Systems Biology, Grenoble, France, 2016, vol. 9957, pp. 128–144.
Kong H, Bartocci E, Bogomolov S, Grosu R, Henzinger TA, Jiang Y, Schilling C. 2016. Discrete abstraction of multiaffine systems. HSB: Hybrid Systems Biology, LNCS, vol. 9957, 128–144.
Kong, Hui, et al. Discrete Abstraction of Multiaffine Systems. Vol. 9957, Springer, 2016, pp. 128–44, doi:10.1007/978-3-319-47151-8_9.