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 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：赋权约束满足问题（VCSPs）构成了一个庞大的计算优化问题类别。近期研究表明，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。本文研究了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-可构造性推广的硬度判定条件，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，数据库理论中研究的联合合取查询（UCQs）弹性问题（在包语义下）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，并示例性地运用本方法解决了文献中一个悬而未决的合取查询复杂度问题。我们推测对于UCQs弹性问题，本文提出的硬度条件与可解性条件具有完备对应关系。此外，我们在包语义下为双向正则路径查询的弹性问题建立了完整的二分定理。