English

Adaptive Boolean Monotonicity Testing in Total Influence Time

Data Structures and Algorithms 2018-01-10 v1 Computational Complexity Discrete Mathematics

Abstract

The problem of testing monotonicity of a Boolean function f:{0,1}n{0,1}f:\{0,1\}^n \to \{0,1\} has received much attention recently. Denoting the proximity parameter by ε\varepsilon, the best tester is the non-adaptive O~(n/ε2)\widetilde{O}(\sqrt{n}/\varepsilon^2) tester of Khot-Minzer-Safra (FOCS 2015). Let I(f)I(f) denote the total influence of ff. We give an adaptive tester whose running time is I(f)poly(ε1logn)I(f)poly(\varepsilon^{-1}\log n).

Cite

@article{arxiv.1801.02816,
  title  = {Adaptive Boolean Monotonicity Testing in Total Influence Time},
  author = {Deeparnab Chakrabarty and C. Seshadhri},
  journal= {arXiv preprint arXiv:1801.02816},
  year   = {2018}
}
R2 v1 2026-06-22T23:40:07.881Z