We study the problem of probabilistic query evaluation on probabilistic graphs, namely, tuple-independent probabilistic databases on signatures of arity two. Our focus is the class of queries that is closed under homomorphisms, or equivalently, the infinite unions of conjunctive queries. Our main result states that all unbounded queries from this class are #P-hard for probabilistic query evaluation. As bounded queries from this class are equivalent to a union of conjunctive queries, they are already classified by the dichotomy of Dalvi and Suciu (2012). Hence, our result and theirs imply a complete data complexity dichotomy, between polynomial time and #P-hardness, for evaluating infinite unions of conjunctive queries over probabilistic graphs. This dichotomy covers in particular all fragments of infinite unions of conjunctive queries such as negation-free (disjunctive) Datalog, regular path queries, and a large class of ontology-mediated queries on arity-two signatures. Our result is shown by reducing from counting the valuations of positive partitioned 2-DNF formulae for some queries, or from the source-to-target reliability problem in an undirected graph for other queries, depending on properties of minimal models. The presented dichotomy result applies to even a special case of probabilistic query evaluation called generalized model counting, where fact probabilities must be 0, 0.5, or 1.

翻译：我们研究对概率图的概率查询评估问题,即关于两个信号的图象的图象独立概率数据库。 我们的焦点是那些在同质主义下封闭的查询类别, 或相同于无限的共交查询的结合。 我们的主要结果显示, 本类的所有无约束查询都是 #P- 硬的, 以便进行概率查询的评价。 本类的受约束查询相当于一个双向查询的结合, 它们已经被Dalvi和Scifiu(2012年)的二分法所分类。 因此, 我们的结果及其结果意味着完全的数据复杂性对齐, 介于多式时间和#P- 硬性之间, 用来评估无限的共交质查询的结合, 而不是比对概率图象的组合。 这种分法特别包括所有无限的连带性查询的片断, 如无否定性(相交错)数据、 定期路径查询, 以及一大批关于异性、 甚至以零调调调的查询。 我们的结果表现为, 从计算可靠度的估值, 也就是根据正分解的2- DF公式的计算结果。