@inproceedings{4d29bc09d5744280871fbe7a9122a580,
title = "Hard properties with (very) short Pcpps and their applications",
abstract = "We show that there exist properties that are maximally hard for testing, while still admitting PCPPs with a proof size very close to linear. Specifically, for every fixed `, we construct a property P(`) ⊆ {0, 1}n satisfying the following: Any testing algorithm for P(`) requires Ω(n) many queries, and yet P(`) has a constant query PCPP whose proof size is O(n · log(`) n), where log(`) denotes the ` times iterated log function (e.g., log(2) n = log log n). The best previously known upper bound on the PCPP proof size for a maximally hard to test property was O(n · polylog n). As an immediate application, we obtain stronger separations between the standard testing model and both the tolerant testing model and the erasure-resilient testing model: for every fixed `, we construct a property that has a constant-query tester, but requires Ω(n/log(`)(n)) queries for every tolerant or erasure-resilient tester.",
keywords = "Coding theory, Erasure resilient testing, PCPP, Property testing, Randomized encoding, Tolerant testing",
author = "Omri Ben-Eliezer and Eldar Fischer and Amit Levi and Rothblum, {Ron D.}",
note = "Publisher Copyright: {\textcopyright} Omri Ben-Eliezer, Eldar Fischer, Amit Levi, and Ron D. Rothblum.; 11th Innovations in Theoretical Computer Science Conference, ITCS 2020 ; Conference date: 12-01-2020 Through 14-01-2020",
year = "2020",
month = jan,
doi = "10.4230/LIPIcs.ITCS.2020.9",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Thomas Vidick",
booktitle = "11th Innovations in Theoretical Computer Science Conference, ITCS 2020",
address = "ألمانيا",
}