{"title":"On Separation by Locally Testable and Locally Threshold Testable Languages","authors":"Thomas Place, L. V. Rooijen, M. Zeitoun","doi":"10.2168/LMCS-10(3:24)2014","DOIUrl":null,"url":null,"abstract":"A separator for two languages is a third language containing the first one\nand disjoint from the second one. We investigate the following decision\nproblem: given two regular input languages, decide whether there exists a\nlocally testable (resp. a locally threshold testable) separator. In both cases,\nwe design a decision procedure based on the occurrence of special patterns in\nautomata accepting the input languages. We prove that the problem is\ncomputationally harder than deciding membership. The correctness proof of the\nalgorithm yields a stronger result, namely a description of a possible\nseparator. Finally, we discuss the same problem for context-free input\nlanguages.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2013-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Logical Methods in Computer Science","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.2168/LMCS-10(3:24)2014","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
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.
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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