Parity games play an important role for LTL synthesis as evidenced by recent breakthroughs on LTL synthesis, which rely in part on parity game solving. Yet state space explosion remains a major issue if we want to scale to larger systems or specifications. In order to combat this problem, we need to investigate symbolic methods such as BDDs, which have been successful in the past to tackle exponentially large systems. It is therefore essential to have symbolic parity game solving algorithms, operating using BDDs, that are fast and that can produce the winning strategies used to synthesize the controller in LTL synthesis. Current symbolic parity game solving algorithms do not yield winning strategies. We now propose two symbolic algorithms that yield winning strategies, based on two recently proposed fixpoint algorithms. We implement the algorithms and empirically evaluate them using benchmarks obtained from SYNTCOMP 2020. Our conclusion is that the algorithms are competitive with or faster than an earlier symbolic implementation of Zielonka's recursive algorithm, while also providing the winning strategies.

中文翻译：

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产生制胜策略的符号平价博弈求解器

奇偶校验游戏在 LTL 合成中发挥着重要作用，最近在 LTL 合成方面的突破证明了这一点，这部分依赖于奇偶校验游戏的求解。然而，如果我们想扩展到更大的系统或规格，状态空间爆炸仍然是一个主要问题。为了解决这个问题，我们需要研究符号方法，例如 BDD，它们过去在处理指数级大型系统方面取得了成功。因此，必须拥有使用 BDD 运行的符号奇偶游戏求解算法，该算法速度快，并且可以产生用于在 LTL 综合中综合控制器的获胜策略。当前的符号奇偶游戏解决算法不会产生获胜策略。我们现在基于最近提出的两个固定点算法提出了两种产生获胜策略的符号算法。