Dichotomy result on 3-regular bipartite non-negative functions

Abstract

We prove a complexity dichotomy theorem for a class of Holant problems on 3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric constraint function f=[x0,x1,x2,x3], we prove that the bipartite Holant problem Holant(f|(=3)) is either computable in polynomial time or #P-hard. The dichotomy criterion on f is explicit.