基于约束的无限图博弈求解方法

Tewodros A. Beyene, Swarat Chaudhuri, C. Popeea, A. Rybalchenko
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引用次数: 88

摘要

我们提出了一种基于约束的方法来计算无限状态规划的状态空间上的双人图博弈中的获胜策略。这种博弈在程序验证和综合中有许多应用,包括无限状态反应程序的合成和无限状态程序的分支时间验证。我们的方法处理由安全性、可达性和一般线性时间逻辑(LTL)属性给出的获胜条件的游戏。对于每个属性类,我们给出一个演绎证明规则,该规则提供了游戏玩家的符号表示,描述了特定玩家的获胜策略。我们的规则是健全的,比较完整的。我们展示了这些规则可以通过使用现成的Horn约束求解器来实现自动化,该约束求解器支持子句头中的存在量化。这些规则的实际应用是通过几个案例研究来证明的,包括一个具有挑战性的“灰姑娘-继母游戏”,允许两个玩家无限地选择离散和连续的选择,以及来自先前程序修复和合成工作的例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A constraint-based approach to solving games on infinite graphs
We present a constraint-based approach to computing winning strategies in two-player graph games over the state space of infinite-state programs. Such games have numerous applications in program verification and synthesis, including the synthesis of infinite-state reactive programs and branching-time verification of infinite-state programs. Our method handles games with winning conditions given by safety, reachability, and general Linear Temporal Logic (LTL) properties. For each property class, we give a deductive proof rule that --- provided a symbolic representation of the game players --- describes a winning strategy for a particular player. Our rules are sound and relatively complete. We show that these rules can be automated by using an off-the-shelf Horn constraint solver that supports existential quantification in clause heads. The practical promise of the rules is demonstrated through several case studies, including a challenging "Cinderella-Stepmother game" that allows infinite alternation of discrete and continuous choices by two players, as well as examples derived from prior work on program repair and synthesis.
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