--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Mária foaf_name: Svoreňová, Mária foaf_surname: Svoreňová - foaf_Person: foaf_givenName: Jan foaf_name: Kretinsky, Jan foaf_surname: Kretinsky foaf_workInfoHomepage: http://www.librecat.org/personId=44CEF464-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-8122-2881 - foaf_Person: foaf_givenName: Martin foaf_name: Chmelik, Martin foaf_surname: Chmelik foaf_workInfoHomepage: http://www.librecat.org/personId=3624234E-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Krishnendu foaf_name: Chatterjee, Krishnendu foaf_surname: Chatterjee foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-4561-241X - foaf_Person: foaf_givenName: Ivana foaf_name: Cěrná, Ivana foaf_surname: Cěrná - foaf_Person: foaf_givenName: Cǎlin foaf_name: Belta, Cǎlin foaf_surname: Belta bibo_doi: 10.1016/j.nahs.2016.04.006 bibo_issue: '2' bibo_volume: 23 dct_date: 2017^xs_gYear dct_identifier: - UT:000390637000014 dct_language: eng dct_publisher: Elsevier@ dct_title: Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games@ ...