Monotonicity Testing
نویسندگان
چکیده
We present improved algorithms for testing monotonicity of functions. Namely, given the ability to query an unknown function f : E' -+ E, where E and E are finite ordered sets, the test always accepts a monotone f and rejects f with high probability if it is e-far from being monotone (i.e., if every monotone function differs from f on more than an E fraction of the domain). For any E > 0, the query complexity of the test is O((n/c) -log|JElog|E|). The previous best known bound was O((n 2 /E) II2 . We also present an alternative test for the boolean range E {0, 1} whose query complexity O(n,/E2) is independent of alphabet size (E. Thesis Supervisor: Michael Sipser Title: Professor of Mathematics
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