{"title":"The regular languages of wire linear AC\\(^0\\)","authors":"Michaël Cadilhac, Charles Paperman","doi":"10.1007/s00236-022-00432-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the regular languages of wire linear <span>\\(\\hbox {AC}^0\\)</span>are characterized as the languages expressible in the two-variable fragment of first-order logic with regular predicates, <span>\\(\\mathrm{FO}^2[\\mathrm{reg}]\\)</span>. Additionally, they are characterized as the languages recognized by the algebraic class <span>\\(\\mathbf {QLDA}\\)</span>. The class is shown to be decidable and examples of languages in and outside of it are presented.</p></div>","PeriodicalId":7189,"journal":{"name":"Acta Informatica","volume":"59 4","pages":"321 - 336"},"PeriodicalIF":0.4000,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Informatica","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s00236-022-00432-2","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the regular languages of wire linear \(\hbox {AC}^0\)are characterized as the languages expressible in the two-variable fragment of first-order logic with regular predicates, \(\mathrm{FO}^2[\mathrm{reg}]\). Additionally, they are characterized as the languages recognized by the algebraic class \(\mathbf {QLDA}\). The class is shown to be decidable and examples of languages in and outside of it are presented.
期刊介绍：
Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics.
Topics of interest include:
• semantics of programming languages
• models and modeling languages for concurrent, distributed, reactive and mobile systems
• models and modeling languages for timed, hybrid and probabilistic systems
• specification, program analysis and verification
• model checking and theorem proving
• modal, temporal, first- and higher-order logics, and their variants
• constraint logic, SAT/SMT-solving techniques
• theoretical aspects of databases, semi-structured data and finite model theory
• theoretical aspects of artificial intelligence, knowledge representation, description logic
• automata theory, formal languages, term and graph rewriting
• game-based models, synthesis
• type theory, typed calculi
• algebraic, coalgebraic and categorical methods
• formal aspects of performance, dependability and reliability analysis
• foundations of information and network security
• parallel, distributed and randomized algorithms
• design and analysis of algorithms
• foundations of network and communication protocols.
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