{"title":"完全和不完全随机NP问题","authors":"Y. Gurevich","doi":"10.1109/SFCS.1987.14","DOIUrl":null,"url":null,"abstract":"A randomized decision problem is a decision problem together with a probability function on the instances. Leonid Levin [Lev1] generalized the NP completeness theory to the case of properly defined randomized NP (shortly, RNP) problems and proved the completeness of a randomized version of the bounded tiling problem with respect to (appropriately generalized) Ptime reductions. Levin's proof naturally splits into two parts; a randomized version of the bounded halting problem is proved complete and then reduced to Randomized Tiling. David Johnson [Jo] provided some intuition behind Levin's definitions and proofs, and challenged readers to find additional natural complete RNP problems.","PeriodicalId":153779,"journal":{"name":"28th Annual Symposium on Foundations of Computer Science (sfcs 1987)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1987-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"43","resultStr":"{\"title\":\"Complete and incomplete randomized NP problems\",\"authors\":\"Y. Gurevich\",\"doi\":\"10.1109/SFCS.1987.14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A randomized decision problem is a decision problem together with a probability function on the instances. Leonid Levin [Lev1] generalized the NP completeness theory to the case of properly defined randomized NP (shortly, RNP) problems and proved the completeness of a randomized version of the bounded tiling problem with respect to (appropriately generalized) Ptime reductions. Levin's proof naturally splits into two parts; a randomized version of the bounded halting problem is proved complete and then reduced to Randomized Tiling. David Johnson [Jo] provided some intuition behind Levin's definitions and proofs, and challenged readers to find additional natural complete RNP problems.\",\"PeriodicalId\":153779,\"journal\":{\"name\":\"28th Annual Symposium on Foundations of Computer Science (sfcs 1987)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1987-10-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"43\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"28th Annual Symposium on Foundations of Computer Science (sfcs 1987)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SFCS.1987.14\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"28th Annual Symposium on Foundations of Computer Science (sfcs 1987)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1987.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 43
摘要
随机决策问题是一个带有实例概率函数的决策问题。Leonid Levin [Lev1]将NP完备性理论推广到适当定义的随机NP(简称RNP)问题，并证明了关于(适当广义的)Ptime约简的有界平铺问题的一个随机版本的完备性。莱文的证明自然分为两部分;证明了有界停止问题的一个随机化版本是完全的，并将其简化为随机化平铺。David Johnson [Jo]在Levin的定义和证明背后提供了一些直觉，并要求读者找到更多的自然完全RNP问题。
A randomized decision problem is a decision problem together with a probability function on the instances. Leonid Levin [Lev1] generalized the NP completeness theory to the case of properly defined randomized NP (shortly, RNP) problems and proved the completeness of a randomized version of the bounded tiling problem with respect to (appropriately generalized) Ptime reductions. Levin's proof naturally splits into two parts; a randomized version of the bounded halting problem is proved complete and then reduced to Randomized Tiling. David Johnson [Jo] provided some intuition behind Levin's definitions and proofs, and challenged readers to find additional natural complete RNP problems.
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