Dichotomy Result on 3-Regular Bipartite Non-negative Functions

11/18/2020

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by   Austen Z. Fan, et al.

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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 = [x_0, x_1, x_2, x_3], 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.