Width-3 Permutation Branching Programs

Abstract

We consider a restricted class of width-3 branching programs where each column of nodes depends on a single variable, and the 0-edges and the 1-edges out of each column form a permutation. In this model, parity and the mod-3 function are easy to calculate, but the and-function is hard. We show that any function of n inputs can be calculated in length O(2^n), and that the and-function in particular requires length O(2^n) if the branching program has one accept node and one reject node.