We present an algorithm for solving two-player safety games that combines a mixed forward/backward search strategy with a symbolic representation of the state space. By combining forward and backward exploration, our algorithm can synthesize strategies that are eager in the sense that they try to prevent progress towards the error states as soon as possible, whereas standard backwards algorithms often produce permissive solutions that only react when absolutely necessary. We provide experimental results for two classes of crafted benchmarks, the benchmark set of the Reactive Synthesis Competition (SYNTCOMP) 2017, as well as a set of randomly generated benchmarks. The results show that our algorithm in many cases produces more eager strategies than a standard backwards algorithm, and solves a number of benchmarks that are intractable for existing tools. Finally, we observe a connection between our algorithm and a recently proposed algorithm for the synthesis of controllers that are robust against disturbances, pointing to possible future applications.

中文翻译：

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一种用于急切策略懒惰综合的符号算法

我们提出了一种解决两人安全博弈的算法，该算法将混合前向/后向搜索策略与状态空间的符号表示相结合。通过结合向前和向后探索，我们的算法可以综合那些急切的策略，因为它们试图尽快阻止错误状态的进展，而标准的向后算法通常会产生仅在绝对必要时做出反应的宽松解决方案。我们为两类精心设计的基准测试提供了实验结果，即反应合成竞赛 (SYNTCOMP) 2017 的基准测试集，以及一组随机生成的基准测试集。结果表明，我们的算法在许多情况下比标准的向后算法产生更多的急切策略，并解决了现有工具难以处理的许多基准测试。最后，我们观察到我们的算法与最近提出的用于合成控制器的算法之间的联系，该算法对干扰具有鲁棒性，指出未来可能的应用。