{"title":"Random strings make hard instances","authors":"H. Buhrman, P. Orponen","doi":"10.1109/SCT.1994.315802","DOIUrl":null,"url":null,"abstract":"We establish the truth of the \"instance complexity conjecture\" in the case of DEXT-complete sets w.r.t. polynomial time computations, and r.e. complete sets w.r.t. recursive computations. Specifically, we obtain for every DEXT-complete set A an exponentially dense subset C such that for every nondecreasing polynomial t(n)=/spl omega/(n log n), ic/sup t/(x:A)/spl ges/K/sup t/(x)-c holds for some constant c and all x/spl isin/C, where ic/sup t/ and K/sup t/ are the t-bounded instance complexity and Kolmogorov complexity measures, respectively. For r.e. complete sets A we obtain an infinite set C/spl sube/A~ such that ic/sup /spl infin(x:A)/spl ges/K/sup /spl infin(x)-c holds for some constant c and all x/spl isin/C. The proofs are based on the observation that Kolmogorov random strings are individually hard to recognize by bounded computations.<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"54 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1994-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SCT.1994.315802","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 17
Abstract
We establish the truth of the "instance complexity conjecture" in the case of DEXT-complete sets w.r.t. polynomial time computations, and r.e. complete sets w.r.t. recursive computations. Specifically, we obtain for every DEXT-complete set A an exponentially dense subset C such that for every nondecreasing polynomial t(n)=/spl omega/(n log n), ic/sup t/(x:A)/spl ges/K/sup t/(x)-c holds for some constant c and all x/spl isin/C, where ic/sup t/ and K/sup t/ are the t-bounded instance complexity and Kolmogorov complexity measures, respectively. For r.e. complete sets A we obtain an infinite set C/spl sube/A~ such that ic/sup /spl infin(x:A)/spl ges/K/sup /spl infin(x)-c holds for some constant c and all x/spl isin/C. The proofs are based on the observation that Kolmogorov random strings are individually hard to recognize by bounded computations.<>