{"title":"逻辑可约性与一元NP","authors":"S. Cosmadakis","doi":"10.1109/SFCS.1993.366882","DOIUrl":null,"url":null,"abstract":"It is shown that, by choosing appropriate encodings of instances as relational structures, several known polynomial-time many-one reductions can he described in first-order logic, and furthermore they are monadic. As a corollary, several known NP-complete problems in monadic NP are shown not to be in monadic co-NP. It is further shown that there is no monadic first-order reduction from connectivity to directed reachability, even in the presence of successor. Finally, some classes of syntactically restricted first-order reductions are shown to be incomparable.<<ETX>>","PeriodicalId":253303,"journal":{"name":"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science","volume":"39 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"22","resultStr":"{\"title\":\"Logical reducibility and monadic NP\",\"authors\":\"S. Cosmadakis\",\"doi\":\"10.1109/SFCS.1993.366882\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is shown that, by choosing appropriate encodings of instances as relational structures, several known polynomial-time many-one reductions can he described in first-order logic, and furthermore they are monadic. As a corollary, several known NP-complete problems in monadic NP are shown not to be in monadic co-NP. It is further shown that there is no monadic first-order reduction from connectivity to directed reachability, even in the presence of successor. Finally, some classes of syntactically restricted first-order reductions are shown to be incomparable.<<ETX>>\",\"PeriodicalId\":253303,\"journal\":{\"name\":\"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science\",\"volume\":\"39 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"22\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1993.366882\",\"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 of 1993 IEEE 34th Annual Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1993.366882","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is shown that, by choosing appropriate encodings of instances as relational structures, several known polynomial-time many-one reductions can he described in first-order logic, and furthermore they are monadic. As a corollary, several known NP-complete problems in monadic NP are shown not to be in monadic co-NP. It is further shown that there is no monadic first-order reduction from connectivity to directed reachability, even in the presence of successor. Finally, some classes of syntactically restricted first-order reductions are shown to be incomparable.<>