ON THE RANDOMNESS COMPLEXITY OF PROPERTY TESTING
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.
randomness complexity property testing weak sources of randomness randomness extractors sampling