Valued constraint satisfaction problems (VCSPs) constitute a large class of computational optimization problems. It was shown recently that, over finite domains, every VCSP is in P or NP-complete, depending on the admitted cost functions. In this article, we study cost functions over countably infinite domains whose automorphisms form an oligomorphic permutation group. Our results include a hardness condition based on a generalization of pp-constructability as known from classical CSPs and a polynomial-time tractability condition based on the concept of fractional polymorphisms. We then observe that the resilience problem for unions of conjunctive queries (UCQs) studied in database theory, under bag semantics, may be viewed as a special case of the VCSPs that we consider. We obtain a complexity dichotomy for the case of incidence-acyclic UCQs and exemplarily use our methods to determine the complexity of a conjunctive query that has been stated as an open problem in the literature. We conjecture that our hardness and tractability conditions match for resilience problems for UCQs. Further, we obtain a complete dichotomy for resilience problems for two-way regular path queries, under bag semantics.

翻译：值约束满足问题（VCSPs）构成了计算优化问题的一大类。最近研究表明，在有限域上，每个VCSP根据所允许的成本函数属于P类或NP完全问题。本文研究可数无限域上的成本函数，其自同构构成寡态置换群。我们的结果包括：基于经典CSP中已知的pp-构造性推广的硬度条件，以及基于分数多态性概念的多项式时间可解性条件。随后我们观察到，数据库理论中研究的联合合取查询（UCQs）韧性问题（在包语义下）可视为我们所考虑VCSP的特例。针对入射无环UCQs情形，我们获得了复杂度二分性结果，并示例性地运用我们的方法确定了文献中一个开放性合取查询的复杂度。我们推测，对于UCQs的韧性问题，我们的硬度条件与可解性条件具有一致性。此外，我们在包语义下获得了双向正则路径查询韧性问题的完整二分性分类。