On Separation by Locally Testable and Locally Threshold Testable Languages

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Logical Methods in Computer Science Pub Date : 2013-08-01 DOI:10.2168/LMCS-10(3:24)2014

Thomas Place, L. V. Rooijen, M. Zeitoun

引用次数: 16

Abstract

A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable (resp. a locally threshold testable) separator. In both cases, we design a decision procedure based on the occurrence of special patterns in automata accepting the input languages. We prove that the problem is computationally harder than deciding membership. The correctness proof of the algorithm yields a stronger result, namely a description of a possible separator. Finally, we discuss the same problem for context-free input languages.

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局部可测试语言与局部阈值可测试语言的分离

两种语言的分隔符是包含第一种语言的第三种语言，并且与第二种语言不相交。我们研究了以下的决策问题:给定两种正则输入语言，判断是否存在局部可测试的(响应)。局部阈值可测试)分隔符。在这两种情况下，我们设计了一个基于接受输入语言的特殊模式自动机的决策过程。我们证明了这个问题在计算上比决定成员更难。该算法的正确性证明产生了一个更强的结果，即对可能分隔符的描述。最后，我们讨论了上下文无关输入语言的相同问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

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.