{"title":"Horn公式等价问题的复杂性。二、","authors":"N. T. Kogabaev","doi":"10.1007/s10469-023-09700-7","DOIUrl":null,"url":null,"abstract":"<div><div><p>We look at the complexity of the existence problem for a Horn sentence equivalent to a given one. It is proved that for a signature consisting of one unary function symbol and any finite number of unary predicate symbols, the problem is computable. For a signature with at least two unary function symbols, it is stated that the problem mentioned is an m-complete <span>\\({\\sum }_{1}^{0}\\mathrm{set}\\)</span>.</p></div></div>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":"61 4","pages":"318 - 327"},"PeriodicalIF":0.4000,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Complexity of the Problem of Being Equivalent to Horn Formulas. II\",\"authors\":\"N. T. Kogabaev\",\"doi\":\"10.1007/s10469-023-09700-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div><p>We look at the complexity of the existence problem for a Horn sentence equivalent to a given one. It is proved that for a signature consisting of one unary function symbol and any finite number of unary predicate symbols, the problem is computable. For a signature with at least two unary function symbols, it is stated that the problem mentioned is an m-complete <span>\\\\({\\\\sum }_{1}^{0}\\\\mathrm{set}\\\\)</span>.</p></div></div>\",\"PeriodicalId\":7422,\"journal\":{\"name\":\"Algebra and Logic\",\"volume\":\"61 4\",\"pages\":\"318 - 327\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra and Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10469-023-09700-7\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10469-023-09700-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
Complexity of the Problem of Being Equivalent to Horn Formulas. II
We look at the complexity of the existence problem for a Horn sentence equivalent to a given one. It is proved that for a signature consisting of one unary function symbol and any finite number of unary predicate symbols, the problem is computable. For a signature with at least two unary function symbols, it is stated that the problem mentioned is an m-complete \({\sum }_{1}^{0}\mathrm{set}\).
期刊介绍：
This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions.
Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences.
All articles are peer-reviewed.
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