We solve the problem of automatically computing a new class of environment assumptions in two-player turn-based finite graph games which characterize an ``adequate cooperation'' needed from the environment to allow the system player to win. Given an $\omega$-regular winning condition $\Phi$ for the system player, we compute an $\omega$-regular assumption $\Psi$ for the environment player, such that (i) every environment strategy compliant with $\Psi$ allows the system to fulfill $\Phi$ (sufficiency), (ii) $\Psi$ can be fulfilled by the environment for every strategy of the system (implementability), and (iii) $\Psi$ does not prevent any cooperative strategy choice (permissiveness). For parity games, which are canonical representations of $\omega$-regular games, we present a polynomial-time algorithm for the symbolic computation of adequately permissive assumptions and show that our algorithm runs faster and produces better assumptions than existing approaches -- both theoretically and empirically. To the best of our knowledge, for $\omega$-regular games, we provide the first algorithm to compute sufficient and implementable environment assumptions that are also permissive.
翻译:我们解决了在双玩者转折游戏中自动计算新一轮环境假设的问题。 双玩者转折游戏需要“ 充分合作” 环境来让系统玩家获胜。 鉴于系统玩家的“ 美元- 美元- 定期赢得条件 $\ Phi$ ”, 我们计算了一个美元- 美元- 定期假设 $\ Psi$ 给环境玩家的“ 美元- 美元- 定期假设 ”, 这样:(一) 每个符合 $\ Psi$ 的环境战略都允许系统满足 $\ Phi$( 充足 ), (二) 美元\ Psi$ 可以通过环境满足系统每一项战略( 实施能力) 的需要, (三) $\ Psi$( 允许性) 并不妨碍任何合作战略选择。 对于平价游戏来说, 美元- 美元- 常规游戏的“ 美元- 普通游戏”, 我们为象征性地计算适当允许的假设提供了一种多边时间算法, 显示我们的算法运行速度比现有方法都快, —— 理论上和实验上都是最好的。 对于我们的知识来说, 对于美元- 最可靠的游戏来说, 我们提供最可靠的算法是足够的环境。