线性时态逻辑的高效归一化

IF 2.3 2区 计算机科学 Q2 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE Journal of the ACM Pub Date : 2024-03-06 DOI:10.1145/3651152
Javier Esparza, Rubén Rubio, Salomon Sickert
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引用次数: 0

摘要

在 80 年代中期,利希滕斯坦、普努埃利和扎克证明了一个经典定理,即过去式 LTL(带有过去算子的 LTL 扩展)的每一个公式都等价于一个形式为 \(\bigwedge _{i=1}^n \mathbf {G}\mathbf {F} 的公式。\varphi _i (vee) (mathbf {F}\mathbf {G}\psi _i ),其中 φi 和 ψi 只包含过去算子。几年后,Chang、Manna 和 Pnueli 在此基础上为 LTL 推导出了类似的正则表达式。这两种正则化程序都有非元素的最坏情况爆炸,并遵循从公式到无反自动机到无星正则表达式再回到公式的复杂路径。我们在这两点上都有所改进。我们提出了 LTL 的直接和纯语法规范化程序,产生了与 Chang、Manna 和 Pnueli 的规范化形式非常相似的规范化形式,它只表现出单次指数膨胀。作为一种应用,我们推导出了一种将 LTL 转化为确定性拉宾自动机的简单算法。该算法将公式规范化,将其转化为特殊的极弱交替自动机,并应用仅对这些特殊自动机有效的简单确定化过程。
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Efficient Normalization of Linear Temporal Logic

In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem stating that every formula of Past LTL (the extension of LTL with past operators) is equivalent to a formula of the form \(\bigwedge _{i=1}^n \mathbf {G}\mathbf {F} \varphi _i \vee \mathbf {F}\mathbf {G} \psi _i \), where φi and ψi contain only past operators. Some years later, Chang, Manna, and Pnueli built on this result to derive a similar normal form for LTL. Both normalization procedures have a non-elementary worst-case blow-up, and follow an involved path from formulas to counter-free automata to star-free regular expressions and back to formulas. We improve on both points. We present direct and purely syntactic normalization procedures for LTL, yielding a normal form very similar to the one by Chang, Manna, and Pnueli, that exhibit only a single exponential blow-up. As an application, we derive a simple algorithm to translate LTL into deterministic Rabin automata. The algorithm normalizes the formula, translates it into a special very weak alternating automaton, and applies a simple determinization procedure, valid only for these special automata.

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来源期刊
Journal of the ACM
Journal of the ACM 工程技术-计算机:理论方法
CiteScore
7.50
自引率
0.00%
发文量
51
审稿时长
3 months
期刊介绍: The best indicator of the scope of the journal is provided by the areas covered by its Editorial Board. These areas change from time to time, as the field evolves. The following areas are currently covered by a member of the Editorial Board: Algorithms and Combinatorial Optimization; Algorithms and Data Structures; Algorithms, Combinatorial Optimization, and Games; Artificial Intelligence; Complexity Theory; Computational Biology; Computational Geometry; Computer Graphics and Computer Vision; Computer-Aided Verification; Cryptography and Security; Cyber-Physical, Embedded, and Real-Time Systems; Database Systems and Theory; Distributed Computing; Economics and Computation; Information Theory; Logic and Computation; Logic, Algorithms, and Complexity; Machine Learning and Computational Learning Theory; Networking; Parallel Computing and Architecture; Programming Languages; Quantum Computing; Randomized Algorithms and Probabilistic Analysis of Algorithms; Scientific Computing and High Performance Computing; Software Engineering; Web Algorithms and Data Mining
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