{"title":"On monadic NP vs. monadic co-NP","authors":"Ronald Fagin, L. Stockmeyer, Moshe Y. Vardi","doi":"10.1109/SCT.1993.336544","DOIUrl":null,"url":null,"abstract":"It is proved that connectivity of finite graphs is not in monadic NP, even in the presence of arbitrary built-in relations of moderate degree (that is, degree (log n) /sup o(1)/). This results in a strong separation between monadic NP and monadic co-NP. The proof uses a combination of three techniques: (1) a technique of W. Hanf (1965) for showing that two (infinite) structures agree on all first-order sentences, under certain conditions; (2) a recent approach to second-order Ehrenfeucht-Fraisse games by M. Ajtai and R. Fagin (1990); and (3) playing Ehrenfeucht-Fraisse games over random structures. Regarding (1), a version of Hanf's result that is better suited for use as a tool in inexpressibility proofs for classes of finite structures is given. The power of these techniques is further demonstrated by using the first two techniques to give a very simple proof of the separation of monadic NP from monadic co-NP without the presence of built-in relations.<<ETX>>","PeriodicalId":331616,"journal":{"name":"[1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"181","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SCT.1993.336544","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 181
Abstract
It is proved that connectivity of finite graphs is not in monadic NP, even in the presence of arbitrary built-in relations of moderate degree (that is, degree (log n) /sup o(1)/). This results in a strong separation between monadic NP and monadic co-NP. The proof uses a combination of three techniques: (1) a technique of W. Hanf (1965) for showing that two (infinite) structures agree on all first-order sentences, under certain conditions; (2) a recent approach to second-order Ehrenfeucht-Fraisse games by M. Ajtai and R. Fagin (1990); and (3) playing Ehrenfeucht-Fraisse games over random structures. Regarding (1), a version of Hanf's result that is better suited for use as a tool in inexpressibility proofs for classes of finite structures is given. The power of these techniques is further demonstrated by using the first two techniques to give a very simple proof of the separation of monadic NP from monadic co-NP without the presence of built-in relations.<>