We consider the problem of finding a homomorphism from an input digraph $G$ to a fixed digraph $H$. We show that if $H$ admits a weak near unanimity polymorphism $\phi$ then deciding whether $G$ admits a homomorphism to $H$ (HOM($H$)) is polynomial-time solvable. This gives proof of the dichotomy conjecture (now dichotomy theorem) by Feder and Vardi. Our approach is combinatorial, and it is simpler than the two algorithms found by Bulatov and Zhuk. We have implemented our algorithm and show some experimental results. We use our algorithm together with the recent result [38] for recognition of Maltsev polymorphisms and decide in polynomial time if a given relational structure $\mathcal{R}$ admits a weak near unanimity polymorphism.
翻译:我们考虑的是从输入量的G$到固定量的H$寻找同质性的问题。 我们显示,如果$H$接受一个微弱的接近全体一致的多式制片的美元, 然后决定$G$是否承认一个同质性到$H(HOM(HOM(H$)))是多元的。 这证明了Feder 和 Vardi 的二分法猜想( (现在的二分法理论) 。 我们的方法是组合式的, 它比Bulatov 和 Zhuk 发现的两个算法简单。 我们实施了我们的算法并展示了一些实验结果。 我们使用我们的算法和最近的结果[38] 来确认Maltsev 多元性, 并在多式时间里决定一个特定的关系结构 $\mathcal{R} 是否承认一个接近一致的多式的虚弱。