This paper investigates regex CQs with string equalities (SERCQs), a subclass of core spanners. As shown by Freydenberger, Kimelfeld, and Peterfreund (PODS 2018), these queries are intractable, even if restricted to acyclic queries. This previous result defines acyclicity by treating regex formulas as atoms. In contrast to this, we propose an alternative definition by converting SERCQs into FC-CQs -- conjunctive queries in FC, a logic that is based on word equations. We introduce a way to decompose word equations of unbounded arity into a conjunction of binary word equations. If the result of the decomposition is acyclic, then evaluation and enumeration of results become tractable. The main result of this work is an algorithm that decides in polynomial time whether an FC-CQ can be decomposed into an acyclic FC-CQ. We also give an efficient conversion from synchronized SERCQs to FC-CQs with regular constraints. As a consequence, tractability results for acyclic relational CQs directly translate to a large class of SERCQs.

中文翻译：

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分裂扳手原子：非循环核心扳手的工具

本文研究具有字符串相等性（SERCQ）的正则表达式CQ，它是核心扳手的子类。如Freydenberger，Kimelfeld和Peterfreund（PODS 2018）所示，即使限于非循环查询，这些查询也很棘手。先前的结果通过将正则表达式视为原子来定义非循环性。与此相反，我们通过将SERCQ转换为FC-CQ提出了另一种定义-FC中的联合查询，FC是基于单词方程的逻辑。我们介绍了一种将无边界的词方程分解为二进制词方程的合集的方法。如果分解的结果是非周期性的，则结果的评估和枚举变得容易处理。这项工作的主要结果是一种算法，该算法可以在多项式时间内确定FC-CQ是否可以分解为非循环FC-CQ。我们还提供了从同步SERCQ到具有常规约束的FC-CQ的高效转换。结果，非循环关系CQ的易处理性结果直接转换为一大类SERCQ。