Paper Info
Title
A Polynomial Lower Bound for Testing Monotonicity.
Abstract
We show that every algorithm for testing n-variate Boolean functions for monotonicityhas query complexity Ω(n1/4). All previous lower bounds for this problem were designed for non-adaptive 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.
Year
DOI
Venue
2016
10.1145/2897518.2897567
STOC
Keywords
DocType
Volume
Property Testing,Adaptivity of query algorithms,Talagrand's Random DNF
Conference
abs/1511.05053
ISSN
Citations 
PageRank 
0737-8017
11
0.73
References 
Authors
15
2
Name
Order
Citations
PageRank
Aleksandrs Belovs113114.50
Eric Blais228622.49