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.

翻译：我们研究具有能源平等目标的随机游戏,这些游戏将数量奖励与质的美元/美元经常条件相结合:最大化的目的是避免能源耗竭,同时满足同等条件。我们发现相应的几乎肯定问题,即是否存在着一个实现能源平等目标的最大化战略,在开始于某一能源水平时,概率为1美元(k美元),是可变的,以美元/cap coNP$(美元)计算。在检查是否存在这种美元和给定的美元最低是否存在时,同样值得考虑。