关于一元NP和一元共NP

[1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference Pub Date : 1993-05-18 DOI:10.1109/SCT.1993.336544

Ronald Fagin, L. Stockmeyer, Moshe Y. Vardi

{"title":"关于一元NP和一元共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":"{\"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}","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

摘要

证明了有限图的连通性在一元NP中是不存在的，即使存在任意中等次(即次(log n) /sup o(1)/)的内嵌关系。这导致单元NP和单元协同NP之间的强烈分离。证明使用了三种技术的组合:(1)W. Hanf(1965)的一种技术，用于证明在某些条件下，两个(无限)结构在所有一阶句子上一致;(2) M. Ajtai和R. Fagin最近提出的二阶Ehrenfeucht-Fraisse博弈方法(1990);(3)在随机结构上玩Ehrenfeucht-Fraisse游戏。关于(1)，给出了一个更适合作为有限结构类不可表达性证明工具的版本。通过使用前两种技术，在不存在内置关系的情况下，给出了一元NP和一元协同NP分离的非常简单的证明，进一步证明了这些技术的强大功能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On monadic NP vs. monadic co-NP

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.<>

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

[1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference

自引率

0.00%

发文量