The Rivest–Vuillemin Conjecture on Monotone Boolean Functions Is True for Ten Variables

A Boolean function f(x1, …, xn) is elusive if every decision tree evaluating f must examine all n variables in the worst case. Rivest and Vuillemin conjectured that every nontrivial monotone weakly symmetric Boolean function is elusive. In this note, we show that this conjecture is true for n=10....

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Bibliographic Details
Published in:Journal of Complexity Vol. 15; no. 4; pp. 526 - 536
Main Authors: Gao, Sui-Xiang, Wu, Weili, Du, Ding-Zhu, Hu, Xiao-Dong
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.1999
Subjects:
Boolean functions
decision trees
elusiveness
Boolean functions
decision trees
elusiveness
ISSN:0885-064X, 1090-2708
Online Access:Get full text
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Summary:A Boolean function f(x1, …, xn) is elusive if every decision tree evaluating f must examine all n variables in the worst case. Rivest and Vuillemin conjectured that every nontrivial monotone weakly symmetric Boolean function is elusive. In this note, we show that this conjecture is true for n=10.
ISSN:0885-064X
1090-2708
DOI:10.1006/jcom.1999.0521