14 research outputs found
A polynomial lower bound for testing monotonicity
We show that every algorithm for testing n-variate Boolean functions for monotonicity has query complexity Ω(n1/4). All previous lower bounds for this problem were designed for nonadaptive algorithms and, as a result, the best previous lower bound for general (possibly adaptive) monotonicity testers was only Ω(logn). Combined with the query complexity of the non-adaptive monotonicity tester of Khot, Minzer, and Safra (FOCS 2015), our lower bound shows that adaptivity can result in at most a quadratic reduction in the query complexity for testing monotonicity. By contrast, we show that there is an exponential gap between the query complexity of adaptive and non-adaptive algorithms for testing regular linear threshold functions (LTFs) for monotonicity. Chen, De, Servedio, and Tan (STOC 2015) recently showed that non-adaptive algorithms require almost Ω(n1/2) queries for this task. We introduce a new adaptive monotonicity testing algorithm which has query complexity O(logn) when the input is a regular LTF
Boolean function monotonicity testing requires (almost) non-adaptive queries
We prove a lower bound of , for all , on the query
complexity of (two-sided error) non-adaptive algorithms for testing whether an
-variable Boolean function is monotone versus constant-far from monotone.
This improves a lower bound for the same problem that
was recently given in [CST14] and is very close to , which we
conjecture is the optimal lower bound for this model