A Boolean function /(x1,x2,…,xn) is said to be elusive, if every decision tree algorithm computing / must examine all n variables in the worst case. In 1988, A.C.C. Yao introduced a question: Is any nontrivial monotone Boolean function that is invariant under the transitive act of group Cm × Cn elusive? The positive answer to this question supports the famous Rivest-Vuillemin conjecture on decision tree complexity. In this paper, we shall partly answer this question.
In present paper, a modified maximum entropy method is proposed to solve minimax problem. This method is a generalization of well-known called maximum entropy method and attempts to overcome some drawbacks of former method. Some properties of new approximate function are presented first and then several numerical examples are given according to modified algorithm, which illustrates that our method is superior to former one.
