{"title":"具有Knuth-Bendix序的项代数的存在论判定程序","authors":"Konstantin Korovin, A. Voronkov","doi":"10.1109/LICS.2000.855777","DOIUrl":null,"url":null,"abstract":"The authors show the decidability of the existential theory of term algebras with any Knuth-Bendix ordering. They achieve this by giving a procedure for solving Knuth-Bendix ordering constraints. As for complexity, NP-hardness of the set of satisfiable quantifier-free formulas can be shown in the same way as by R. Nieuwenhuis (1993). The algorithm presented does not give an NP upper bound; we point out parts of our algorithm that may cause nonpolynomial behavior.","PeriodicalId":300113,"journal":{"name":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","volume":"266 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2000-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"26","resultStr":"{\"title\":\"A decision procedure for the existential theory of term algebras with the Knuth-Bendix ordering\",\"authors\":\"Konstantin Korovin, A. Voronkov\",\"doi\":\"10.1109/LICS.2000.855777\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The authors show the decidability of the existential theory of term algebras with any Knuth-Bendix ordering. They achieve this by giving a procedure for solving Knuth-Bendix ordering constraints. As for complexity, NP-hardness of the set of satisfiable quantifier-free formulas can be shown in the same way as by R. Nieuwenhuis (1993). The algorithm presented does not give an NP upper bound; we point out parts of our algorithm that may cause nonpolynomial behavior.\",\"PeriodicalId\":300113,\"journal\":{\"name\":\"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)\",\"volume\":\"266 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2000-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"26\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/LICS.2000.855777\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.2000.855777","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A decision procedure for the existential theory of term algebras with the Knuth-Bendix ordering
The authors show the decidability of the existential theory of term algebras with any Knuth-Bendix ordering. They achieve this by giving a procedure for solving Knuth-Bendix ordering constraints. As for complexity, NP-hardness of the set of satisfiable quantifier-free formulas can be shown in the same way as by R. Nieuwenhuis (1993). The algorithm presented does not give an NP upper bound; we point out parts of our algorithm that may cause nonpolynomial behavior.
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