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A List by Author: Jan Krčál

e-mail:
krcal(a)fi.muni.cz

Stochastic Real-Time Games with Qualitative Timed Automata Objectives

by Tomáš Brázdil, Jan Krčál, Jan Křetínský, Antonín Kučera, Vojtěch Řehák, A full version of the paper presented at CONCUR 2010. August 2010, 39 pages.

FIMU-RS-2010-05. Available as Postscript, PDF.

Abstract:

We consider two-player stochastic games over real-time probabilistic processes where the winning objective is specified by a timed automaton. The goal of player I is to play in such a way that the play (a timed word) is accepted by the timed automaton with probability one. Player II aims at the opposite. We prove that whenever player I has a winning strategy, then she also has a strategy that can be specified by a timed automaton. The strategy automaton reads the history of a play, and the decisions taken by the strategy depend only on the region of the resulting configuration. We also give an exponential-time algorithm which computes a winning timed automaton strategy if it exists.

Continuous-Time Stochastic Games with Time-Bounded Reachability

by Tomáš Brázdil, Vojtěch Forejt, Jan Krčál, Jan Křetínský, Antonín Kučera, A full version of the paper presented at FST&TCS 2009. October 2009, 46 pages.

FIMU-RS-2009-09. Available as Postscript, PDF.

Abstract:

We study continuous-time stochastic games with time-bounded reachability objectives. We show that each vertex in such a game has a value (i.e., an equilibrium probability), and we classify the conditions under which optimal strategies exist. Finally, we show how to compute optimal strategies in finite uniform games, and how to compute e-optimal strategies in finitely-branching games with bounded rates (for finite games, we provide detailed complexity estimations).