arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1802.00758cs.LO
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反应合成中策略的决策树表示

Strategy Representation by Decision Trees in Reactive Synthesis

Tomáš Brázdil, Krishnendu Chatterjee, Jan Křetínský, Viktor Toman

摘要:

在计算机科学中,两个参与者在有限状态图上进行的图博弈是许多问题的核心。特别地,具有$ω$ -正则获胜条件的图博弈,可以表达安全性、活性、公平性等属性,是反应系统验证和综合的基本框架。在图博弈的不同状态下,参与者的决策被表示为策略。虽然解决具有奇偶目标的图游戏的算法问题已经被广泛研究,但图游戏中最突出的策略表示数据结构是二元决策图(BDD)。然而,由于位级表示,BDD不保留策略决策的固有风味,并且众所周知难以最小化以获得简洁的表示。在这项工作中,我们提出了决策树的战略表示图游戏。决策树保留了策略决策的味道,并允许基于熵的最小化得到简洁的树。然而,决策树在设置中工作(例如,概率模型),其中允许误差,并且通常避免数据的过拟合。相反,对于图博弈中的策略,不允许有错误,并且决策树必须代表整个策略。我们开发新的技术来扩展决策树,以克服上述障碍,同时保留基于熵的技术,以获得简洁的树。我们已经实现了我们的技术来扩展现有的决策树求解器。我们目前的实验结果表明,决策树的反应合成的问题提供了一个更有效的数据结构的战略表示相比,BDD。

英文摘要:

Graph games played by two players over finite-state graphs are central in many problems in computer science. In particular, graph games with $ω$-regular winning conditions, specified as parity objectives, which can express properties such as safety, liveness, fairness, are the basic framework for verification and synthesis of reactive systems. The decisions for a player at various states of the graph game are represented as strategies. While the algorithmic problem for solving graph games with parity objectives has been widely studied, the most prominent data-structure for strategy representation in graph games has been binary decision diagrams (BDDs). However, due to the bit-level representation, BDDs do not retain the inherent flavor of the decisions of strategies, and are notoriously hard to minimize to obtain succinct representation. In this work we propose decision trees for strategy representation in graph games. Decision trees retain the flavor of decisions of strategies and allow entropy-based minimization to obtain succinct trees. However, decision trees work in settings (e.g., probabilistic models) where errors are allowed, and overfitting of data is typically avoided. In contrast, for strategies in graph games no error is allowed, and the decision tree must represent the entire strategy. We develop new techniques to extend decision trees to overcome the above obstacles, while retaining the entropy-based techniques to obtain succinct trees. We have implemented our techniques to extend the existing decision tree solvers. We present experimental results for problems in reactive synthesis to show that decision trees provide a much more efficient data-structure for strategy representation as compared to BDDs.

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