A o(n) monotonicity tester for boolean functions over the hypercube
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Optimal bounds for monotonicity and lipschitz testing over hypercubes and hypergrids
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On Approximating the Number of Relevant Variables in a Function
ACM Transactions on Computation Theory (TOCT)
Partial tests, universal tests and decomposability
Proceedings of the 5th conference on Innovations in theoretical computer science
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We develop a new technique for proving lower bounds in property testing, by showing a strong connection between testing and communication complexity. We give a simple scheme for reducing communication problems to testing problems, thus allowing us to use known lower bounds in communication complexity to prove lower bounds in testing. This scheme is general and implies a number of new testing bounds, as well as simpler proofs of several known bounds. For the problem of testing whether a Boolean function is k-linear (a parity function on k variables), we achieve a lower bound of Ω(k) queries, even for adaptive algorithms with two-sided error, thus confirming a conjecture of Goldreich (2010a). The same argument behind this lower bound also implies a new proof of known lower bounds for testing related classes such as k-juntas. For some classes, such as the class of monotone functions and the class of s-sparse GF(2) polynomials, we significantly strengthen the best known bounds.