An Improved Pseudo-Polynomial Upper Bound for the Value Problem and Optimal Strategy Synthesis in Mean Payoff Games

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

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 mean-payoff 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 algor…

A Convex Programming-based Algorithm for Mean Payoff Stochastic Games with Perfect Information

We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph $G = (V, E)$, with local rewards $r: E \to \ZZ$, and three types of positions: black $V_B$, white $V_W$, and random $V_R$ forming a partition of $V$. It is a long-standing open question whether a polynomial time algorithm for BWR-games exists, even when $|V_R|=0$. In fact, a pseudo-polynomial algorithm for BWR-games would already imply their polynomial solvability. In this short note, we show that BWR-games can be solved via convex programming in pseudo-polynomial time if the…

Faster O(|V|^2|E|W)-Time Energy Algorithms for Optimal Strategy Synthesis in Mean Payoff Games

This study strengthens the links between Mean Payoff Games (\MPG{s}) and Energy Games (EG{s}). Firstly, we offer a faster $O(|V|^2|E|W)$ pseudo-polynomial time and $Θ(|V|+|E|)$ space deterministic algorithm for solving the Value Problem and Optimal Strategy Synthesis in \MPG{s}. This improves the best previously known estimates on the pseudo-polynomial time complexity to: \[ O(|E|\log |V|) + Θ\Big(\sum_{v\in V}\texttt{deg}_Γ(v)\cdot\ell_Γ(v)\Big) = O(|V|^2|E|W), \] where $\ell_Γ(v)$ counts the number of times that a certain energy-lifting operator $δ(\cdot, v)$ is applied to any $v\in V$, alon…

Symblicit algorithms for optimal strategy synthesis in monotonic Markov decision processes (extended version)

When treating Markov decision processes (MDPs) with large state spaces, using explicit representations quickly becomes unfeasible. Lately, Wimmer et al. have proposed a so-called symblicit algorithm for the synthesis of optimal strategies in MDPs, in the quantitative setting of expected mean-payoff. This algorithm, based on the strategy iteration algorithm of Howard and Veinott, efficiently combines symbolic and explicit data structures, and uses binary decision diagrams as symbolic representation. The aim of this paper is to show that the new data structure of pseudo-antichains (an extension …

勘误：《能量博弈与平均支付博弈的更快确定性指数时间算法》

Errata to: "Faster Deterministic Exponential Time Algorithm for Energy Games and Mean Payoff Games"

本技术报告针对ICALP 19提出的能量博弈与平均支付博弈改进指数时间算法的伪代码错误，给出修正版算法并更正相关引理证明。

符号算法在单调马尔可夫决策过程中的最优策略综合

Symblicit algorithms for optimal strategy synthesis in monotonic Markov decision processes

本文提出基于伪反链的符号算法，用于解决单调马尔可夫决策过程中的最优策略综合问题，适用于期望均值收益和随机最短路径两种量化设置，并在自动规划和LTL综合中展现出良好的性能。