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arXiv 2011.091102020-11-18cs.CC

Dichotomy Result on 3-Regular Bipartite Non-negative Functions

Austen Z. Fan, Jin-Yi Cai

备注：: 13 pages, 2 figures

英文摘要：

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 $\operatorname{Holant} \left( f \mid \left( =_3 \right) \right)$ is \emph{either} computable in polynomial time \emph{or} $\#$P-hard. The dichotomy criterion on $f$ is explicit.

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