Two-sided error proximity oblivious testing

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 ǫ-far from having the property are accepted with probability at most c − F(ǫ), where F : (0, 1] → (0, 1] 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 ∈ (0, 1]. We show that, in many natural cases, two-sided error...

• Type: Journal
• Year: 2016
• Where: RSA
• Authors: Oded Goldreich, Igor Shinkar
• Keywords: RSA 2016