Operational consistent query answering (CQA) is a recent framework for CQA based on revised definitions of repairs, which are built by applying a sequence of operations (e.g., fact deletions) starting from an inconsistent database until we reach a database that is consistent w.r.t. the given set of constraints. It has been recently shown that there are efficient approximations for computing the percentage of repairs, as well as of sequences of operations leading to repairs, that entail a given query when we focus on primary keys, conjunctive queries, and assuming the query is fixed (i.e., in data complexity). However, it has been left open whether such approximations exist when the query is part of the input (i.e., in combined complexity). We show that this is the case when we focus on self-join-free conjunctive queries of bounded generelized hypertreewidth. We also show that it is unlikely that efficient approximation schemes exist once we give up one of the adopted syntactic restrictions, i.e., self-join-freeness or bounding the generelized hypertreewidth. Towards the desired approximation schemes, we introduce a novel counting complexity class, called SpanTL, show that each problem in SpanTL admits an efficient approximation scheme by using a recent approximability result in the context of tree automata, and then place the problems of interest in SpanTL.

翻译：操作一致性查询回答（CQA）是一种基于修复定义修正的最新框架，该框架通过从非一致性数据库开始依次执行一系列操作（例如删除事实）来构建修复，直至达到与给定约束集一致的数据库。近期研究表明，当聚焦于主键、合取查询并假设查询固定时（即数据复杂度），存在高效近似方法可计算修复序列（以及导致修复的操作序列）中蕴含给定查询的比例。然而，当查询作为输入的一部分时（即组合复杂度），此类近似方法是否存在仍为开放问题。我们证明，在关注有界广义超树宽的无自连接合取查询时，该问题可解。同时表明，一旦放弃所采用的两项语法限制（即无自连接性或广义超树宽有界性），高效近似方案的存在性将变得不可能。为构建预期近似方案，我们引入了一种新的计数复杂度类SpanTL，证明SpanTL中的每个问题均能通过利用树自动机领域的最新可近似性结论获得高效近似方案，进而将目标问题归入SpanTL类中。