Temporal logic control for stochastic linear systems using
abstraction refinement of probabilistic games

J 2017

Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games

SVOREŇOVÁ, Mária, Jan KŘETÍNSKÝ, Martin CHMELÍK, Krishnendu CHATTERJEE, Ivana ČERNÁ et. al.

Basic information

Original name

Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games

Authors

SVOREŇOVÁ, Mária (703 Slovakia, belonging to the institution), Jan KŘETÍNSKÝ (203 Czech Republic, guarantor, belonging to the institution), Martin CHMELÍK (203 Czech Republic), Krishnendu CHATTERJEE (356 India), Ivana ČERNÁ (203 Czech Republic, belonging to the institution) and Calin BELTA (642 Romania)

Edition

Nonlinear Analysis: Hybrid Systems, Elsevier, 2017, 1751-570X

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 4.010

RIV identification code

RIV/00216224:14330/17:00094586

Organization unit

Faculty of Informatics

DOI

http://dx.doi.org/10.1016/j.nahs.2016.04.006

UT WoS

000390637000014

Keywords in English

probabilistic systems; verification; games; temporal logic

Abstract

V originále

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.

Links

GA15-17564S, research and development project

Name: Teorie her jako prostředek pro formální analýzu a verifikaci počítačových systémů

Investor: Czech Science Foundation

MUNI/A/0897/2016, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace VI.

Investor: Masaryk University, Category A

Citovat

SVOREŇOVÁ, Mária, Jan KŘETÍNSKÝ, Martin CHMELÍK, Krishnendu CHATTERJEE, Ivana ČERNÁ and Calin BELTA. Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games. Nonlinear Analysis: Hybrid Systems. Elsevier, 2017, vol. 23, February 2017, p. 230-253. ISSN 1751-570X. Available from: https://dx.doi.org/10.1016/j.nahs.2016.04.006.

@article{1365664,
   author = {Svoreňová, Mária and Křetínský, Jan and Chmelík, Martin and Chatterjee, Krishnendu and Černá, Ivana and Belta, Calin},
   article_number = {February 2017},
   doi = {http://dx.doi.org/10.1016/j.nahs.2016.04.006},
   keywords = {probabilistic systems; verification; games; temporal logic},
   language = {eng},
   issn = {1751-570X},
   journal = {Nonlinear Analysis: Hybrid Systems},
   title = {Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games},
   volume = {23},
   year = {2017}
}

TY  - JOUR
ID  - 1365664
AU  - Svoreňová, Mária - Křetínský, Jan - Chmelík, Martin - Chatterjee, Krishnendu - Černá, Ivana - Belta, Calin
PY  - 2017
TI  - Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games
JF  - Nonlinear Analysis: Hybrid Systems
VL  - 23
IS  - February 2017
SP  - 230-253
EP  - 230-253
PB  - Elsevier
SN  - 1751570X
KW  - probabilistic systems
KW  - verification
KW  - games
KW  - temporal logic
N2  - 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.
ER  -

SVOREŇOVÁ, Mária, Jan KŘETÍNSKÝ, Martin CHMELÍK, Krishnendu CHATTERJEE, Ivana ČERNÁ and Calin BELTA. Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games. \textit{Nonlinear Analysis: Hybrid Systems}. Elsevier, 2017, vol.~23, February 2017, p.~230-253. ISSN~1751-570X. Available from: https://dx.doi.org/10.1016/j.nahs.2016.04.006.

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