发表机构
University of Tartu（塔尔图大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究一致查询回答的组合复杂性，针对带一元主键、无环攻击图的布尔无自连接合取查询，证明键-非键图源SCC数有界时该问题为多项式时间，无界时为Π₂^P完全。
AI 中文摘要
在过去二十年中，一致查询回答的数据复杂性已得到广泛研究。本文研究了较少受到关注的组合复杂性问题，其输入由完整性约束集合、（可能不一致的）数据库和查询组成，任务是确定数据库关于约束的所有修复是否满足该查询。本文旨在分离使该问题计算上可处理的查询特定结构特征，重点关注主键约束上的布尔无自连接合取查询，因为在此背景下对应的复杂性问题已被完全分类；此外，本文仅关注具有无环攻击图的查询，这类查询恰好是那些可接受一阶重写的查询；作为额外简化假设，本文聚焦于一元主键。每个带一元主键的合取查询自然会产生一个有向图，本文称之为键-非键图，其中每个原子贡献一条从其键变量到每个非键变量的边。本文的主要结果是，在上述假设下，当键-非键图中的源强连通分量（SCC）数量受常数界限时，一致查询回答的组合复杂性处于多项式时间内；为证明该结果，本文开发了变量防护、攻击传播图等新概念，以及数据库与查询饱和、查询归一化等技术。此外，若无该有界限制，该问题的组合复杂性被证明是Π₂^P完全的。
英文摘要
We study the combined complexity of consistent query answering for Boolean self-join-free conjunctive queries with unary primary keys and acyclic attack graphs. Although every fixed query in this class admits a first-order rewriting [21], we show that allowing the query to vary makes the problem Pi_2^P-complete. To isolate the query structure governing this transition, we introduce the closure generator size: the minimum number of query variables whose closure under the functional dependencies induced by the primary keys contains every query variable. Our main theorem shows that every fixed bound on this parameter yields polynomial-time combined complexity. Parameterized by the closure generator size, the problem is in XP and co-W[t]-hard for every fixed t. The polynomial-time result is specific to unary primary keys: with binary primary keys, the problem becomes coNP-hard already for self-join-free queries with acyclic attack graphs and closure generator size zero. Regarding the upper bound, CQA is in coNP for arbitrary Boolean conjunctive queries of bounded closure treewidth or bounded hyperclosure treewidth; these width measures originate in [1]. Our polynomial-time algorithm realizes quantifier alternation dynamically by interleaving existential and universal substitutions with variable-level reductions. To implement this approach, we introduce concepts and techniques such as attack-propagation graphs, variable guarding and guarded pruning, database and query saturation, and query normalization.
