Valued constraint satisfaction problems (VCSPs) constitute a large class of computational optimisation 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 generalisation 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 query that had remained open in the literature. Further, we conjecture that our hardness and tractability conditions match for resilience problems for UCQs.

翻译：价值约束满足问题（VCSPs）构成了计算优化问题的一大类别。最近研究表明，在有限域上，每个VCSP根据所允许的成本函数不同，要么属于P类问题，要么是NP完全问题。本文研究定义在可数无限域上的成本函数，其自同构构成一个寡态置换群。我们的研究成果包括：基于经典CSP中已知的pp-可构造性概念的广义化提出的硬度判定条件，以及基于分数多态性概念的多项式时间可解性判定条件。随后我们观察到，在数据库理论中研究的联合合取查询（UCQs）的韧性问题（采用包语义时）可视为本文所考虑VCSP的特例。我们针对入射无环UCQs情形获得了复杂度二分定理，并示例性地运用我们的方法确定了文献中悬而未决的某个查询的复杂度。此外，我们推测对于UCQs的韧性问题，本文提出的硬度条件与可解性条件具有对应性。