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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Vydáno v:Journal of Complexity Ročník 15; číslo 4; s. 526 - 536
Hlavní autoři: Gao, Sui-Xiang, Wu, Weili, Du, Ding-Zhu, Hu, Xiao-Dong
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.12.1999
Témata:
Boolean functions
decision trees
elusiveness
Boolean functions
decision trees
elusiveness
ISSN:0885-064X, 1090-2708
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Popis
Shrnutí: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