2016-06-19
A polynomial lower bound for testing monotonicity
Publication
Publication
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.
| Additional Metadata | |
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| doi.org/10.1145/2897518.2897567 | |
| Annual ACM Symposium on Theory of Computing | |
| Organisation | Algorithms and Complexity |
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Belovs, A., & Blais, E. (Eric). (2016). A polynomial lower bound for testing monotonicity. doi:10.1145/2897518.2897567 |
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