文章基本信息

标题：Two-Sided Error Proximity Oblivious Testing
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作者：Oded Goldreich, Igor Shinkar
期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2012
卷号：2012
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：Loosely speaking, a proximity-oblivious (property) tester is a randomized algorithm that makes a constant number of queries to a tested object and distinguishes objects that have a predetermined property from those that lack it. Specifically, for some threshold probability c, objects having the property are accepted with probability at least c, whereas objects that are \e-far from having the property are accepted with probability at most c−F(\e), where F:(01](01] is some fixed monotone function. (We stress that, in contrast to standard testers, a proximity-oblivious tester is not given the proximity parameter.) The foregoing notion, introduced by Goldreich and Ron (STOC 2009), was originally defined with respect to c=1, which corresponds to one-sided error (proximity-oblivious) testing. Here we study the two-sided error version of proximity-oblivious testers; that is, the (general) case of arbitrary c(01] . We show that, in many natural cases, two-sided error proximity-oblivious testers are more powerful than one-sided error proximity-oblivious testers; that is, many natural properties that have no one-sided error proximity-oblivious testers do have a two-sided error proximity-oblivious tester.