
A decision tree of a Boolean function \(f\) is a rooted binary tree, whose nonleaf vertices are labeled by its variables, and leaves are labeled by \(0\) and \(1\). Edges are labeled such that edges from a nonleaf vertex to its successors are labeled by \(0\) and \(1\), respectively, and every variable appears at most once in an path from the root to a leaf. Given an assignment to variables of a Boolean function \(f(x_1, x_2,\dots, x_n)\), the function \(f\) can be computed by its decision tree. A Boolean function \(f(x_1, x_2,\dots, x_n)\) is called elusive if every decision tree computing \(f\) must examine \(n\) variables in the worst case. It ist a long-standing conjecture that every nontrivial monotone weakly symmetric Boolean function is elusive. In this paper, every Boolean function with twelve variables is proved to be elusive.
Monotone Boolean function, Boolean function, Decision tree, Elusive, Complexity classes (hierarchies, relations among complexity classes, etc.), Discrete Mathematics and Combinatorics, Combinatorics in computer science, Boolean functions, Graphs and abstract algebra (groups, rings, fields, etc.), Theoretical Computer Science
Monotone Boolean function, Boolean function, Decision tree, Elusive, Complexity classes (hierarchies, relations among complexity classes, etc.), Discrete Mathematics and Combinatorics, Combinatorics in computer science, Boolean functions, Graphs and abstract algebra (groups, rings, fields, etc.), Theoretical Computer Science
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