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.
翻译:我们证明,在3个普通双边图中,对一组无足轻重的问题,我们有一个复杂的二分法理论。鉴于一个任意的非负加权对称约束函数$f = [x_0, x_1, x_2, x_2, x_3]$,我们证明,双边对齐问题$\operatorname{Holant}\left(f\mid\left( ⁇ 3\right)\right)$是计算多元时/emph{or}${ ⁇ $_$_P-hard。$f$的对齐标准是明确的。