Splitting Spanner Atoms: A Tool for Acyclic Core Spanners

TL;DR

This paper introduces a method to decompose complex word equations into simpler parts, enabling efficient evaluation of certain regex-based conjunctive queries by identifying when they are acyclic.

Contribution

It proposes a polynomial-time algorithm to determine if an FC-CQ can be decomposed into an acyclic form, facilitating tractable query evaluation.

Findings

Decomposition of word equations into binary form is possible for acyclic cases.

Evaluation and enumeration become tractable for acyclic FC-CQs.

Conversion from synchronized SERCQs to FC-CQs preserves tractability.

Abstract

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.