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A tighter relation between sensitivity complexity and certificate complexity

文献类型：期刊论文

作者He, Kun2,3; Li, Qian1; Sun, Xiaoming2,3
刊名THEORETICAL COMPUTER SCIENCE
出版日期2019-03-01
卷号762页码:1-12
关键词Sensitivity conjecture Sensitivity Block sensitivity Certificate complexity Boolean functions
ISSN号0304-3975
DOI10.1016/j.tcs.2018.08.025
英文摘要The sensitivity conjecture proposed by Nisan and Szegedy in 1994, which asserts that for any Boolean function, its sensitivity complexity is polynomially related to the block sensitivity complexity, is one of the most important and challenging problems in the study of decision tree complexity, Despite a lot of efforts, the best known upper bound of block sensitivity, as well as the certificate complexity, is still exponential in terms of sensitivity. In this paper, we give a better upper bound for certificate complexity and block sensitivity, bs(f) <= C(f) <= (8/9 +0(1))s(f)2(s(f)-1)where bs(f), C(f) and s(f) are the block sensitivity, certificate complexity and sensitivity, respectively. The proof is based on a deep investigation on the structure of the sensitivity graph. We also provide a tighter relationship between the 0-certificate complexity C-0(f) and 0-sensitivity s(0)(f) for functions with small 1-sensitivity s(1)(f). (C) 2018 Elsevier B.V. All rights reserved.
资助项目National Natural Science Foundation of China[61433014] ; National Natural Science Foundation of China[61502449] ; National Natural Science Foundation of China[61602440] ; 973 Program of China[2016YFB1000201] ; China National Program for support of Top-notch Young Professionals
WOS研究方向Computer Science
语种英语
WOS记录号WOS:000459528200001
出版者ELSEVIER SCIENCE BV
源URL[http://119.78.100.204/handle/2XEOYT63/3418]  
专题中国科学院计算技术研究所期刊论文_英文
通讯作者He, Kun
作者单位1.Alibaba Grp, Hangzhou 310052, Zhejiang, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
3.Chinese Acad Sci, Inst Comp Technol, CAS Key Lab Network Data Sci & Technol, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 He, Kun,Li, Qian,Sun, Xiaoming. A tighter relation between sensitivity complexity and certificate complexity[J]. THEORETICAL COMPUTER SCIENCE,2019,762:1-12.
APA He, Kun,Li, Qian,&Sun, Xiaoming.(2019).A tighter relation between sensitivity complexity and certificate complexity.THEORETICAL COMPUTER SCIENCE,762,1-12.
MLA He, Kun,et al."A tighter relation between sensitivity complexity and certificate complexity".THEORETICAL COMPUTER SCIENCE 762(2019):1-12.

入库方式： OAI收割

来源：计算技术研究所

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