{"title":"Complexity of the Problem of Being Equivalent to Horn Formulas","authors":"N. T. Kogabaev","doi":"10.1007/s10469-022-09665-z","DOIUrl":null,"url":null,"abstract":"<div><div><p>We look at the complexity of the existence problem for a Horn sentence (identity, quasi-identity, ∀-sentence, ∃-sentence) equivalent to a given one. It is proved that if the signature contains at least one symbol of arity k ≥ 2, then each of the problems mentioned is an m-complete <span>\\( {\\Sigma}_1^0 \\)</span> set.</p></div></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10469-022-09665-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We look at the complexity of the existence problem for a Horn sentence (identity, quasi-identity, ∀-sentence, ∃-sentence) equivalent to a given one. It is proved that if the signature contains at least one symbol of arity k ≥ 2, then each of the problems mentioned is an m-complete \( {\Sigma}_1^0 \) set.
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