基于整数oracle的实数P对NP问题

2016 Dynamics of Systems, Mechanisms and Machines (Dynamics) Pub Date : 2016-11-01 DOI:10.1109/DYNAMICS.2016.7819075

A. Rybalov

{"title":"基于整数oracle的实数P对NP问题","authors":"A. Rybalov","doi":"10.1109/DYNAMICS.2016.7819075","DOIUrl":null,"url":null,"abstract":"Relativized complexity classes are actively studied in the computation complexity theory since 1975. Classical result of Baker, Gill and Solovay states that there exist two oracles A and B such that PA = NPA, but PB ≠ NPB. This result indicates that the classical tools of theory of algorithms (such as diagonalization) are inapplicable to prove the inequality P ≠ NP. We consider a relativised Blum-Shub-Smale model of computations over the field of real numbers. We prove that relativized complexity classes PZ and NPZ are different in this model, where the oracle Z is the set of integers.","PeriodicalId":293543,"journal":{"name":"2016 Dynamics of Systems, Mechanisms and Machines (Dynamics)","volume":"58 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the P vs NP problem over reals with integer oracle\",\"authors\":\"A. Rybalov\",\"doi\":\"10.1109/DYNAMICS.2016.7819075\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Relativized complexity classes are actively studied in the computation complexity theory since 1975. Classical result of Baker, Gill and Solovay states that there exist two oracles A and B such that PA = NPA, but PB ≠ NPB. This result indicates that the classical tools of theory of algorithms (such as diagonalization) are inapplicable to prove the inequality P ≠ NP. We consider a relativised Blum-Shub-Smale model of computations over the field of real numbers. We prove that relativized complexity classes PZ and NPZ are different in this model, where the oracle Z is the set of integers.\",\"PeriodicalId\":293543,\"journal\":{\"name\":\"2016 Dynamics of Systems, Mechanisms and Machines (Dynamics)\",\"volume\":\"58 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2016 Dynamics of Systems, Mechanisms and Machines (Dynamics)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/DYNAMICS.2016.7819075\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 Dynamics of Systems, Mechanisms and Machines (Dynamics)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DYNAMICS.2016.7819075","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

自1975年以来，相对复杂性类在计算复杂性理论中得到了积极的研究。Baker, Gill和Solovay的经典结果表明，存在两个预言A和B，使得PA = NPA，但PB≠NPB。这一结果表明经典的算法理论工具(如对角化)不适用于证明不等式P≠NP。我们考虑了实数域上计算的一个相对化blum - shub - small模型。在此模型中，我们证明了相对复杂性类PZ和NPZ是不同的，其中oracle Z是整数的集合。

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 the P vs NP problem over reals with integer oracle

Relativized complexity classes are actively studied in the computation complexity theory since 1975. Classical result of Baker, Gill and Solovay states that there exist two oracles A and B such that P^A = NP^A, but P^B ≠ NP^B. This result indicates that the classical tools of theory of algorithms (such as diagonalization) are inapplicable to prove the inequality P ≠ NP. We consider a relativised Blum-Shub-Smale model of computations over the field of real numbers. We prove that relativized complexity classes P^Z and NP^Z are different in this model, where the oracle Z is the set of integers.

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

2016 Dynamics of Systems, Mechanisms and Machines (Dynamics)

自引率

0.00%

发文量