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On the randomness complexity of property testing. (English) Zbl 1204.68097
Summary: 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.

68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
68W20 Randomized algorithms
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