article published yes Mária Svoreňová author Jan Kretinsky author 44CEF464-F248-11E8-B48F-1D18A9856A870000-0002-8122-2881 Martin Chmelik author 3624234E-F248-11E8-B48F-1D18A9856A87 Krishnendu Chatterjee author 2E5DCA20-F248-11E8-B48F-1D18A9856A870000-0002-4561-241X Ivana Cěrná author Cǎlin Belta author ToHe department KrCh department International IST Postdoc Fellowship Programme project Quantitative Reactive Modeling project Quantitative Graph Games: Theory and Applications project Rigorous Systems Engineering project Modern Graph Algorithmic Techniques in Formal Verification project Game Theory project We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study. Elsevier2017 eng 1410.5387 00039063700001410.1016/j.nahs.2016.04.006 232230 - 253 https://research-explorer.ista.ac.at/record/1689 M. Svoreňová, J. Kretinsky, M. Chmelik, K. Chatterjee, I. Cěrná, and C. Belta, “Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games,” <i>Nonlinear Analysis: Hybrid Systems</i>, vol. 23, no. 2. Elsevier, pp. 230–253, 2017. Svoreňová, Mária, Jan Kretinsky, Martin Chmelik, Krishnendu Chatterjee, Ivana Cěrná, and Cǎlin Belta. “Temporal Logic Control for Stochastic Linear Systems Using Abstraction Refinement of Probabilistic Games.” <i>Nonlinear Analysis: Hybrid Systems</i>. Elsevier, 2017. <a href="https://doi.org/10.1016/j.nahs.2016.04.006">https://doi.org/10.1016/j.nahs.2016.04.006</a>. Svoreňová, M., Kretinsky, J., Chmelik, M., Chatterjee, K., Cěrná, I., &#38; Belta, C. (2017). Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games. <i>Nonlinear Analysis: Hybrid Systems</i>. Elsevier. <a href="https://doi.org/10.1016/j.nahs.2016.04.006">https://doi.org/10.1016/j.nahs.2016.04.006</a> Svoreňová M, Kretinsky J, Chmelik M, Chatterjee K, Cěrná I, Belta C. 2017. Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games. Nonlinear Analysis: Hybrid Systems. 23(2), 230–253. Svoreňová M, Kretinsky J, Chmelik M, Chatterjee K, Cěrná I, Belta C. Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games. <i>Nonlinear Analysis: Hybrid Systems</i>. 2017;23(2):230-253. doi:<a href="https://doi.org/10.1016/j.nahs.2016.04.006">10.1016/j.nahs.2016.04.006</a> M. Svoreňová, J. Kretinsky, M. Chmelik, K. Chatterjee, I. Cěrná, C. Belta, Nonlinear Analysis: Hybrid Systems 23 (2017) 230–253. Svoreňová, Mária, et al. “Temporal Logic Control for Stochastic Linear Systems Using Abstraction Refinement of Probabilistic Games.” <i>Nonlinear Analysis: Hybrid Systems</i>, vol. 23, no. 2, Elsevier, 2017, pp. 230–53, doi:<a href="https://doi.org/10.1016/j.nahs.2016.04.006">10.1016/j.nahs.2016.04.006</a>. 14072018-12-11T11:51:50Z2025-06-11T06:33:00Z