Abstract Linear Temporal Logic over finite traces ( LTL f ) was proposed in 2013 and has attracted increasing interest around the AI community. Though the theoretic basis for LTL f has been thoroughly explored since that time, there are still few algorithmic tools that are able to provide an efficient reasoning strategy for LTL f . In this paper, we present a SAT-based framework for LTL f satisfiability checking, which is the foundation of LTL f reasoning. We use propositional SAT-solving techniques to construct a transition system, which is an automata-style structure, for an input LTL f formula; satisfiability checking is then reduced to a path-search problem over this transition system. Based on this framework, we further present CDLSC (Conflict-Driven LTL f Satisfiability Checking), a novel algorithm (heuristic) that leverages information produced by propositional SAT solvers, utilizing both satisfiability and unsatisfiability results. More specifically, the satisfiable results of the SAT solver are used to create new states of the transition system and the unsatisfiable results to accelerate the path search over the system. We evaluate all 5 off-the-shelf LTL f satisfiability algorithms against our new approach CDLSC . Based on a comprehensive evaluation over 4 different LTL f benchmark suits with a total amount of 9317 formulas, our time-cost analysis shows that 1) CDLSC performs best on checking unsatisfiable formulas by achieving approximately a 4X time speedup, compared to the second-best solution (K-LIVE [1] ); 2) Although no approaches dominate checking satisfiable formulas, CDLSC performs best on 2 of the total 4 tested satisfiable benchmark suits; and 3) CDLSC gains the best overall performance when considering both satisfiable and unsatisfiable instances.

中文翻译：

---

基于 SAT 的显式 LTLf 可满足性检查

摘要 有限轨迹上的线性时序逻辑 (LTL f) 于 2013 年提出，引起了 AI 社区越来越多的兴趣。虽然从那时起 LTL f 的理论基础已经被彻底探索，但仍然很少有算法工具能够为 LTL f 提供有效的推理策略。在本文中，我们提出了一个基于 SAT 的 LTL f 可满足性检查框架，这是 LTL f 推理的基础。我们使用命题 SAT 求解技术为输入 LTL f 公式构建一个转换系统，这是一种自动机式结构；然后将可满足性检查简化为该过渡系统上的路径搜索问题。基于这个框架，我们进一步提出了 CDLSC（Conflict-Driven LTL f Satisfiability Checking），一种新颖的算法（启发式），它利用命题 SAT 求解器产生的信息，利用可满足性和不可满足性结果。更具体地说，SAT求解器的可满足结果用于创建过渡系统的新状态，不可满足结果用于加速系统上的路径搜索。我们针对我们的新方法 CDLSC 评估了所有 5 个现成的 LTL f 可满足性算法。基于对总共 9317 个公式的 4 个不同 LTL f 基准套件的综合评估，我们的时间成本分析表明：1) CDLSC 通过实现大约 4 倍的时间加速，在检查不可满足的公式方面表现最佳，与第二好的相比解决方案（K-LIVE [1]）；2）虽然没有任何方法可以支配检查可满足的公式，CDLSC 在 4 个可满足基准套装中的 2 个上表现最好；3) CDLSC 在考虑可满足和不可满足实例时获得最佳的整体性能。