{"title":"Automata Presenting Structures: A Survey of the Finite String Case","authors":"S. Rubin","doi":"10.2178/bsl/1208442827","DOIUrl":null,"url":null,"abstract":"Abstract A structure has a (finite-string) automatic presentation if the elements of its domain can be named by finite strings in such a way that the coded domain and the coded atomic operations are recognised by synchronous multitape automata. Consequently, every structure with an automatic presentation has a decidable first-order theory. The problems surveyed here include the classification of classes of structures with automatic presentations, the complexity of the isomorphism problem, and the relationship between definability and recognisability.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"169 - 209"},"PeriodicalIF":1.1000,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1208442827","citationCount":"109","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of Symbolic Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2178/bsl/1208442827","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 109
Abstract
Abstract A structure has a (finite-string) automatic presentation if the elements of its domain can be named by finite strings in such a way that the coded domain and the coded atomic operations are recognised by synchronous multitape automata. Consequently, every structure with an automatic presentation has a decidable first-order theory. The problems surveyed here include the classification of classes of structures with automatic presentations, the complexity of the isomorphism problem, and the relationship between definability and recognisability.
期刊介绍：
The Bulletin of Symbolic Logic was established in 1995 by the Association for Symbolic Logic to provide a journal of high standards that would be both accessible and of interest to as wide an audience as possible. It is designed to cover all areas within the purview of the ASL: mathematical logic and its applications, philosophical and non-classical logic and its applications, history and philosophy of logic, and philosophy and methodology of mathematics.
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