Random polynomial time is equal to slightly-random polynomial time

U. Vazirani, V. Vazirani
{"title":"Random polynomial time is equal to slightly-random polynomial time","authors":"U. Vazirani, V. Vazirani","doi":"10.1109/SFCS.1985.45","DOIUrl":null,"url":null,"abstract":"Random Polynomial Time (Rp) is currently considered to be the class of tractable computational problems. Here one assumes a source of truly random bits. However, the known sources of randomness are imperfect. They can be modeled as an adversary source, called slightly-random source. Slightlyrandom Polynomial Time (SRp) is the class of problems solvable in polynomial time using such a source. SRp is thus a more realistic definition of a tractable computational problem. In this paper we give an affirmative answer to the question \"is Rp = SRp?\" Our proof method is constructive: given an Rp algorithm for a problem, we show how to obtain an SRp algorithm for it. Studying the relationship between randomized and deterministic computation is currently an important issue. A central question here is \"is Rp = P?\" Our result may be a step towards answering this question.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"2 7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"101","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1985.45","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 101

Abstract

Random Polynomial Time (Rp) is currently considered to be the class of tractable computational problems. Here one assumes a source of truly random bits. However, the known sources of randomness are imperfect. They can be modeled as an adversary source, called slightly-random source. Slightlyrandom Polynomial Time (SRp) is the class of problems solvable in polynomial time using such a source. SRp is thus a more realistic definition of a tractable computational problem. In this paper we give an affirmative answer to the question "is Rp = SRp?" Our proof method is constructive: given an Rp algorithm for a problem, we show how to obtain an SRp algorithm for it. Studying the relationship between randomized and deterministic computation is currently an important issue. A central question here is "is Rp = P?" Our result may be a step towards answering this question.
随机多项式时间等于稍微随机多项式时间
随机多项式时间(Rp)目前被认为是一类可处理的计算问题。这里我们假设一个真正随机的比特的来源。然而,已知的随机性来源是不完善的。它们可以被建模为对手源,称为微随机源。微随机多项式时间(SRp)是一类可以在多项式时间内解决的问题。因此,SRp是可处理计算问题的更现实的定义。本文对“Rp = SRp吗?”这个问题给出了肯定的回答。我们的证明方法是建设性的:给定一个问题的Rp算法,我们展示了如何获得该问题的SRp算法。研究随机计算和确定性计算之间的关系是当前的一个重要问题。这里的核心问题是“Rp = P吗?”我们的研究结果可能是朝着回答这个问题迈出的一步。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信