conference paper published yes Hui Kong author 3BDE25AA-F248-11E8-B48F-1D18A9856A870000-0002-3066-6941 Ezio Bartocci author Sergiy Bogomolov author 369D9A44-F248-11E8-B48F-1D18A9856A870000-0002-0686-0365 Radu Grosu author Thomas A Henzinger author 40876CD8-F248-11E8-B48F-1D18A9856A870000−0002−2985−7724 Yu Jiang author Christian Schilling author 3A2F4DCE-F248-11E8-B48F-1D18A9856A870000-0003-3658-1065 ToHe department HSB: Hybrid Systems Biology Formal methods for the design and analysis of complex systems project Rigorous Systems Engineering project 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. https://research-explorer.ista.ac.at/download/1227/4840/IST-2017-781-v1+1_main.pdf application/pdfno Springer2016Grenoble, France eng 00038992810000910.1007/978-3-319-47151-8_9 9957128 - 144 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. <a href="https://doi.org/10.1007/978-3-319-47151-8_9">https://doi.org/10.1007/978-3-319-47151-8_9</a>. Kong, H., Bartocci, E., Bogomolov, S., Grosu, R., Henzinger, T. A., Jiang, Y., &#38; Schilling, C. (2016). Discrete abstraction of multiaffine systems (Vol. 9957, pp. 128–144). Presented at the HSB: Hybrid Systems Biology, Grenoble, France: Springer. <a href="https://doi.org/10.1007/978-3-319-47151-8_9">https://doi.org/10.1007/978-3-319-47151-8_9</a> Kong, Hui, et al. <i>Discrete Abstraction of Multiaffine Systems</i>. Vol. 9957, Springer, 2016, pp. 128–44, doi:<a href="https://doi.org/10.1007/978-3-319-47151-8_9">10.1007/978-3-319-47151-8_9</a>. H. Kong <i>et al.</i>, “Discrete abstraction of multiaffine systems,” presented at the HSB: Hybrid Systems Biology, Grenoble, France, 2016, vol. 9957, pp. 128–144. H. Kong, E. Bartocci, S. Bogomolov, R. Grosu, T.A. Henzinger, Y. Jiang, C. Schilling, in:, Springer, 2016, 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 H, Bartocci E, Bogomolov S, et al. Discrete abstraction of multiaffine systems. In: Vol 9957. Springer; 2016:128-144. doi:<a href="https://doi.org/10.1007/978-3-319-47151-8_9">10.1007/978-3-319-47151-8_9</a> 12272018-12-11T11:50:49Z2025-09-22T09:24:50Z