On the Randomness Complexity of Property Testing

Authors:
Oded Goldreich;Or Sheffet
Affiliations:
Weizmann Institute of Science, Rehovot, Israel;Weizmann Institute of Science, Rehovot, Israel
Venue:
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2007

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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.