Perfect-Information Stochastic Mean-Payoff Parity Games

Chatterjee, Krishnendu; Doyen, Laurent; Gimbert, Hugo; Oualhadj, Youssouf

doi:10.1007/978-3-642-54830-7_14

Cited by 11 publications

(11 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We believe that our techniques can be adapted to also produce optimal strategies for both players (i.e., the strategies that secure the value that we show how to compute). Another direction for future work is improving the complexity of solving stochastic mean-payoff parity games [5].…”

Section: Resultsmentioning

confidence: 99%

A pseudo-quasi-polynomial algorithm for mean-payoff parity games

Daviaud

Jurdziński

Lazić

2018

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science

View full text Add to dashboard Cite

In a mean-payoff parity game, one of the two players aims both to achieve a qualitative parity objective and to minimize a quantitative long-term average of payoffs (aka. mean payoff). The game is zero-sum and hence the aim of the other player is to either foil the parity objective or to maximize the mean payoff.Our main technical result is a pseudo-quasi-polynomial algorithm for solving meanpayoff parity games. All algorithms for the problem that have been developed for over a decade have a pseudo-polynomial and an exponential factors in their running times; in the running time of our algorithm the latter is replaced with a quasi-polynomial one. By the results of Chatterjee and Doyen (2012) and of Schewe, Weinert, and Zimmermann (2018), our main technical result implies that there are pseudo-quasipolynomial algorithms for solving parity energy games and for solving parity games with weights.Our main conceptual contributions are the definitions of strategy decompositions for both players, and a notion of progress measures for mean-payoff parity games that generalizes both parity and energy progress measures. The former provides normal forms for and succinct representations of winning strategies, and the latter enables the application to mean-payoff parity games of the order-theoretic machinery that underpins a recent quasi-polynomial algorithm for solving parity games.

show abstract

Section: Resultsmentioning

confidence: 99%

A pseudo-quasi-polynomial algorithm for mean-payoff parity games

Daviaud

Jurdziński

Lazić

2018

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science

View full text Add to dashboard Cite

show abstract

“…We showed that several almost-sure problems for combined energy-parity objectives in simple stochastic games are in NP ∩ coNP. No pseudo-polynomial algorithm is known (just like for stochastic mean-payoff parity games [20]). All these problems subsume (stochastic) parity games, by setting all rewards to 0.…”

Section: Discussionmentioning

confidence: 99%

“…Stochastic mean-payoff parity games were studied in [20], where it was shown that they can be solved in NP ∩ coNP. However, this does not imply a solution for stochastic energy-parity games, since, unlike in the non-stochastic case [16], there is no known reduction from energy-parity to mean-payoff parity in stochastic games.…”

Section: Introductionmentioning

confidence: 99%

Simple Stochastic Games with Almost-Sure Energy-Parity Objectives are in NP and coNP

Mayr

Schewe

Totzke

et al. 2021

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We study stochastic games with energy-parity objectives, which combine quantitative rewards with a qualitative $$\omega $$ ω -regular condition: The maximizer aims to avoid running out of energy while simultaneously satisfying a parity condition. We show that the corresponding almost-sure problem, i.e., checking whether there exists a maximizer strategy that achieves the energy-parity objective with probability 1 when starting at a given energy level k, is decidable and in $$\mathsf {NP}\cap \mathsf {coNP}$$ NP ∩ coNP . The same holds for checking if such a k exists and if a given k is minimal.

show abstract

“…Illustration. In the example of Figure 4, a solution to the linear program gives for instance f 1 = 1 16 and f 3 = 7 16 , which corresponds to a randomized memoryless strategy that chooses from s 1 to go to s 2 with probability 1 1+7 = 1 8 and to go to {s 3 , s 4 } with probability 7 1+7 = 7 8 . This strategy satisfies the conjunction of mean-payoff objectives with probability 1 (it ensures that the long-run average of the rewards is 1 32 ≥ 0 in both dimensions).…”

Section: Generalized Mean-payoff Objectives Under Finitememory In Mdpsmentioning

confidence: 99%

Perfect-Information Stochastic Games with Generalized Mean-Payoff Objectives

Chatterjee

Doyen

2016

Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science

Self Cite

View full text Add to dashboard Cite

Graph games provide the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic reactive processes, the traditional model is perfect-information stochastic games, where some transitions of the game graph are controlled by two adversarial players, and the other transitions are executed probabilistically. We consider such games where the objective is the conjunction of several quantitative objectives (specified as mean-payoff conditions), which we refer to as generalized mean-payoff objectives. The basic decision problem asks for the existence of a finite-memory strategy for a player that ensures the generalized mean-payoff objective be satisfied with a desired probability against all strategies of the opponent. A special case of the decision problem is the almost-sure problem where the desired probability is 1. Previous results presented a semi-decision procedure for ε-approximations of the almostsure problem. In this work, we show that both the almost-sure problem as well as the general basic decision problem are coNP-complete, significantly improving the previous results. Moreover, we show that in the case of 1-player stochastic games, randomized memoryless strategies are sufficient and the problem can be solved in polynomial time. In contrast, in two-player stochastic games, we show that even with randomized strategies exponential memory is required in general, and present a matching exponential upper bound. We also study the basic decision problem with infinite-memory strategies and present computational complexity results for the problem. Our results are relevant in the synthesis of stochastic reactive systems with multiple quantitative requirements. *

show abstract

Perfect-Information Stochastic Mean-Payoff Parity Games

Cited by 11 publications

References 29 publications

A pseudo-quasi-polynomial algorithm for mean-payoff parity games

A pseudo-quasi-polynomial algorithm for mean-payoff parity games

Simple Stochastic Games with Almost-Sure Energy-Parity Objectives are in NP and coNP

Perfect-Information Stochastic Games with Generalized Mean-Payoff Objectives

Contact Info

Product

Resources

About