We study stochastic games with energy-parity objectives, which combine quantitative rewards with a qualitative $\omega$-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 $NP \cap coNP$. The same holds for checking if such a $k$ exists and if a given $k$ is minimal.

中文翻译：

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具有几乎确定的能量平价目标的简单随机游戏位于NP和coNP中

我们研究具有能量平价目标的随机博弈，该博弈将定量奖励与定性的\\ omega $常规条件相结合：最大化器的目的是在满足同等条件的同时避免耗尽能量。我们证明了相应的几乎确定的问题，即检查是否存在最大化器策略，该策略在给定能量水平$ k $时以概率$ 1 $达到能量奇偶性目标，是可确定的，并且在$ NP \ cap coNP中$。检查这样的$ k $是否存在以及给定的$ k $是否最小同样适用。