J. Gallier, Wayne Snyder, P. Narendran, D. Plaisted
{"title":"刚性e统一是np完全的","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":"{\"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}","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}
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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