On The Randomness Complexity of Property Testing

Authors:
Oded Goldreich;Or Sheffet
Affiliations:
Weizmann Institute of Science, Department of Computer Science, Rehovot, Israel;Carnegie Mellon University, Department of Computer Science, Pittsburgh, USA
Venue:
Computational Complexity
Year:
2010

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On the average-case complexity of property testing

Studies in complexity and cryptography

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Abstract

We initiate a general study of the randomness complexity of property testing, aimed at reducing the randomness complexity of testers without (significantly) increasing their query complexity. One concrete motivation for this study is provided by the observation that the product of the randomness and query complexity of a tester determine the actual query complexity of implementing a version of this tester that utilizes a weak source of randomness (through a randomness-extractor). We present rather generic upper and lower bounds on the randomness complexity of property testing and study in depth the special case of testing bipartiteness in two standard property testing models.