Rivest-Vuillemin conjecture is true for monotone boolean functions with twelve variables

Authors:
Sui-Xiang Gao;Ding-Zhu Du;xiao-Dong Hun;Xiaohua Jia
Affiliations:
Department of Mathematics, Graduate School at Beijing, University of Science and Technology of China, Beijing 100039, China;Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong;Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN;lnstitute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China
Venue:
Discrete Mathematics
Year:
2002

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Abstract

A Boolean function f(x1,x2,...,xn) is elusive if every decision tree computing f must examine all n variables in the worst case. It is a long-standing conjecture that every nontrivial monotone weakly symmetric Boolean function is elusive. In this paper, we prove this conjecture for Boolean functions with twelve variables.