A very simple function that requires exponential size read-once branching programs

Abstract

A Boolean function in n variables is presented that is computable in depth 2 monotone AC 0 and has prime implicants of length 2 only but requires 2 Ω(√n) size read-once branching programs. The function considered is defined using (1, 1)-disjoint Boolean sums and the solution of the famous problem of Zarankiewicz.