Determinacy and optimal strategies in infinite-state stochastic reachability games

Broek, VáClav

doi:10.1016/j.tcs.2012.10.038

Cited by 2 publications

(4 citation statements)

References 11 publications

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“…It was shown in [4] and [18] (and also follows as a corollary from [5]) that finitely branching games with reachability objectives with any threshold ✄c with c ∈ [0, 1] are strongly determined. In contrast, strong determinacy does not hold for infinitely branching reachability games with thresholds ✄c with c ∈ (0, 1); cf.…”

Section: B Reachability and Safetymentioning

confidence: 99%

“…Let us review the finitely branching case. Quantitative reachability games are strongly determined [18], [4], [5]. They are generally not strongly FR-determined [19], but they are strongly MD-determined under any of the conditions provided by Theorem 5.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

“…However, most these works used techniques that are specially adapted to the underlying automata model, not a general analysis of infinite-state games. Some results on general stochastic games with countably infinite state spaces were presented in [19], [4], [18], [5] though many questions remained open (see our contributions further below).…”

Section: Introductionmentioning

confidence: 99%

“…Strong determinacy in infinite games. It was shown in [4], [18], [5] that in finitely branching games with countable state spaces reachability objectives with any threshold ✄c with c ∈ [0, 1], are strongly determined. However, the player ✷ strategy may need infinite memory [19], and thus reachability objectives are not strongly MD determined.…”

Section: Introductionmentioning

confidence: 99%

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On strong determinacy of countable stochastic games

Kiefer

Mayr

Shirmohammadi

et al. 2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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We study 2-player turn-based perfect-information stochastic games with countably infinite state space. The players aim at maximizing/minimizing the probability of a given event (i.e., measurable set of infinite plays), such as reachability, Büchi, ω-regular or more general objectives.These games are known to be weakly determined, i.e., they have value. However, strong determinacy of threshold objectives (given by an event E and a threshold c ∈ [0, 1]) was open in many cases: is it always the case that the maximizer or the minimizer has a winning strategy, i.e., one that enforces, against all strategies of the other player, that E is satisfied with probability ≥ c (resp. < c)?We show that almost-sure objectives (where c = 1) are strongly determined. This vastly generalizes a previous result on finite games with almost-sure tail objectives. On the other hand we show that ≥ 1/2 (co-)Büchi objectives are not strongly determined, not even if the game is finitely branching.Moreover, for almost-sure reachability and almost-sure Büchi objectives in finitely branching games, we strengthen strong determinacy by showing that one of the players must have a memoryless deterministic (MD) winning strategy.

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Section: B Reachability and Safetymentioning

confidence: 99%