Testing versus estimation of graph properties
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Tolerant locally testable codes
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Distance approximation in bounded-degree and general sparse graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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A property tester with high probability accepts inputs satisfying a given property and rejects inputs that are far from satisfying it. A tolerant property tester, as defined by Parnas, Ron and Rubinfeld, must also accept inputs that are close enough to satisfying the property.We construct two properties of binary functions for which there exists a test making a constant number of queries, but yet there exists no such tolerant test. The first construction uses Hadamard codes and long codes. Then, using Probabilistically Checkable Proofs of Proximity as constructed by Ben-Sasson et. al., we exhibit a property which has constant query intolerant testers but for which any tolerant tester requires n^驴(1) queries.