J. Gallier, Wayne Snyder, P. Narendran, D. Plaisted
{"title":"Rigid E-unification is NP-complete","authors":"J. Gallier, Wayne Snyder, P. Narendran, D. Plaisted","doi":"10.1109/LICS.1988.5121","DOIUrl":null,"url":null,"abstract":"Rigid E-unification is a restricted kind of unification modulo equational theories, or E-unification, that arises naturally in extending P. Andrews' (1981) theorem-proving method of mating to first-order languages with equality. It is shown that rigid E-unification is NP-complete and that finite complete sets of rigid E-unifiers always exist. As a consequence, deciding whether a family of mated sets is an equational mating is an NP-complete problem. Some implications of this result regarding the complexity of theorem proving in first-order logic with equality are discussed.<<ETX>>","PeriodicalId":425186,"journal":{"name":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"39","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.1988.5121","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 39
Abstract
Rigid E-unification is a restricted kind of unification modulo equational theories, or E-unification, that arises naturally in extending P. Andrews' (1981) theorem-proving method of mating to first-order languages with equality. It is shown that rigid E-unification is NP-complete and that finite complete sets of rigid E-unifiers always exist. As a consequence, deciding whether a family of mated sets is an equational mating is an NP-complete problem. Some implications of this result regarding the complexity of theorem proving in first-order logic with equality are discussed.<>
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