On the Sensitivity Complexity of k -Uniform Hypergraph Properties

Author:

Li Qian1,Sun Xiaoming2

Affiliation:

1. Shenzhen University, Shenzhen, China

2. University of Chinese Academy of Sciences, Beijing, China

Abstract

In this article, we investigate the sensitivity complexity of hypergraph properties. We present a k -uniform hypergraph property with sensitivity complexity O ( n (⌈ k/3 ⌉) for any k3 , where n is the number of vertices. Moreover, we can do better when k1 (mod 3) by presenting a k -uniform hypergraph property with sensitivity O (n⌈ k/3 ⌉-1/2). This result disproves a conjecture of Babai, which conjectures that the sensitivity complexity of k -uniform hypergraph properties is at least Ω ( n k/2 ). We also investigate the sensitivity complexity of other symmetric functions and show that for many classes of transitive Boolean functions the minimum achievable sensitivity complexity can be O (N 1/3 ), where N is the number of variables.

Funder

National Natural Science Foundation of China

Strategic Priority Research Program of Chinese Academy of Sciences

973 Program of China

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Theory and Mathematics,Theoretical Computer Science

Reference23 articles.

1. New separation between s(f) and bs(f);Ambainis Andris;Electronic Colloquium on Computational Complexity,2011

2. Joshua Biderman Kevin Cuddy Ang Li and Min Jae Song. 2015. On the sensitivity of k-uniform hypergraph properties. arXiv:1510.00354 Joshua Biderman Kevin Cuddy Ang Li and Min Jae Song. 2015. On the sensitivity of k-uniform hypergraph properties. arXiv:1510.00354

3. Monotone Properties of k-Uniform Hypergraphs are Weakly Evasive

4. Complexity measures and decision tree complexity: a survey

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