推理符号自动机

IF 0.6 4区 数学 Q4 COMPUTER SCIENCE, THEORY & METHODS Logical Methods in Computer Science Pub Date : 2023-04-20 DOI:10.46298/lmcs-19(2:5)2023
Dana Fisman, Hadar Frenkel, Sandra Zilles
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引用次数: 0

摘要

我们研究了符号有限状态自动机(SFA)的可学习性,这是一个在软件验证中得到广泛应用的模型。关于该主题的最新文献遵循查询学习范式,到目前为止所有获得的结果都是积极的。在此范例中,我们提供了sfa有效可学习性的必要条件,并由此得到了第一个否定结果。本文研究的重点是在多项式时间和数据的极限识别范式下,sfa的可学习性及其有效可识别性的增强,这涉及到学习者可以从中正确推断目标语言的一组系统特征样本的存在。我们给出了用多项式时间和数据在极限下识别sfa的必要条件,以及sfa有效可学习性的充分条件。从这些条件中我们推导出一个正结果和一个负结果。学习算法的性能通常是目标语言表示大小的函数。由于sfa通常没有规范的形式,并且在转换谓词的复杂性和转换数量之间存在权衡,因此我们首先定义sfa的大小度量。我们重新审视了sfa程序的复杂性,并根据这些措施对其进行了分析,重点讨论了sfa的特殊形式:归一化sfa和整齐sfa,以及单调有效布尔代数上的sfa。这是CSL'22上发表的同名论文的扩展版。
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Inferring Symbolic Automata
We study the learnability of symbolic finite state automata (SFA), a model shown useful in many applications in software verification. The state-of-the-art literature on this topic follows the query learning paradigm, and so far all obtained results are positive. We provide a necessary condition for efficient learnability of SFAs in this paradigm, from which we obtain the first negative result. The main focus of our work lies in the learnability of SFAs under the paradigm of identification in the limit using polynomial time and data, and its strengthening efficient identifiability, which are concerned with the existence of a systematic set of characteristic samples from which a learner can correctly infer the target language. We provide a necessary condition for identification of SFAs in the limit using polynomial time and data, and a sufficient condition for efficient learnability of SFAs. From these conditions we derive a positive and a negative result. The performance of a learning algorithm is typically bounded as a function of the size of the representation of the target language. Since SFAs, in general, do not have a canonical form, and there are trade-offs between the complexity of the predicates on the transitions and the number of transitions, we start by defining size measures for SFAs. We revisit the complexity of procedures on SFAs and analyze them according to these measures, paying attention to the special forms of SFAs: normalized SFAs and neat SFAs, as well as to SFAs over a monotonic effective Boolean algebra. This is an extended version of the paper with the same title published in CSL'22.
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来源期刊
Logical Methods in Computer Science
Logical Methods in Computer Science 工程技术-计算机:理论方法
CiteScore
1.80
自引率
0.00%
发文量
105
审稿时长
6-12 weeks
期刊介绍: Logical Methods in Computer Science is a fully refereed, open access, free, electronic journal. It welcomes papers on theoretical and practical areas in computer science involving logical methods, taken in a broad sense; some particular areas within its scope are listed below. Papers are refereed in the traditional way, with two or more referees per paper. Copyright is retained by the author. Topics of Logical Methods in Computer Science: Algebraic methods Automata and logic Automated deduction Categorical models and logic Coalgebraic methods Computability and Logic Computer-aided verification Concurrency theory Constraint programming Cyber-physical systems Database theory Defeasible reasoning Domain theory Emerging topics: Computational systems in biology Emerging topics: Quantum computation and logic Finite model theory Formalized mathematics Functional programming and lambda calculus Inductive logic and learning Interactive proof checking Logic and algorithms Logic and complexity Logic and games Logic and probability Logic for knowledge representation Logic programming Logics of programs Modal and temporal logics Program analysis and type checking Program development and specification Proof complexity Real time and hybrid systems Reasoning about actions and planning Satisfiability Security Semantics of programming languages Term rewriting and equational logic Type theory and constructive mathematics.
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