# On Rivest-Vuillemin Conjecture for Fourteen Variables

## TL;DR

This paper proves the Rivest-Vuillemin conjecture for 14-variable boolean functions, showing that all nontrivial monotone weakly symmetric functions with 14 variables are elusive, meaning all variables must be checked in the worst case.

## Contribution

The paper confirms the Rivest-Vuillemin conjecture for the case of 14 variables, advancing understanding of elusive functions in boolean function theory.

## Key findings

- The conjecture holds for n=14 variables.
- All nontrivial monotone weakly symmetric functions with 14 variables are elusive.
- The result extends previous partial verifications of the conjecture.

## Abstract

A boolean function $f(x_1,...,x_n)$ is \textit{weakly symmetric} if it is invariant under a transitive permutation group on its variables. A boolean function $f(x_1,...,x_n)$ is \textit{elusive} if we have to check all $x_1$,..., $x_n$ to determine the output of $f(x_1,...,x_n)$ in the worst-case. It is conjectured that every nontrivial monotone weakly symmetric boolean function is elusive, which has been open for a long time. In this paper, we report that this conjecture is true for $n=14$.