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

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Abstract:

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. Copyright 1999 Academic Press.

Keywords: Boolean functions; decision trees; elusiveness

Document Type: Research Article

Affiliations: 1: Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, 100080, People's Republic of China 2: Department of Computer Science and Engineering, University of Minnesota, Minneapolis, Minnesota, 55455 3: Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong, China

Publication date: December 1, 1999

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