Boundedness for Unions of Conjunctive Regular Path Queries over Simple Regular Expressions

TL;DR

This paper investigates the boundedness problem for unions of conjunctive regular path queries (UCRPQs) over simple regular expressions, establishing complexity results and methods for producing equivalent bounded queries.

Contribution

It provides a detailed complexity analysis of the boundedness problem for UCRPQs with simple regexes and introduces polynomial-time methods for bounded query production.

Findings

Boundedness problem for UCRPQs with simple regexes is $oldsymbol{ ext{Π}^P_2}$-complete.

Equivalent bounded queries can be generated in polynomial time when they exist.

Finding maximally bounded queries when unbounded is feasible in $oldsymbol{ ext{Π}^P_2}$.

Abstract

The problem of checking whether a recursive query can be rewritten as query without recursion is a fundamental reasoning task, known as the boundedness problem. Here we study the boundedness problem for Unions of Conjunctive Regular Path Queries (UCRPQs), a navigational query language extensively used in ontology and graph database querying. The boundedness problem for UCRPQs is ExpSpace-complete. Here we focus our analysis on UCRPQs using simple regular expressions, which are of high practical relevance and enjoy a lower reasoning complexity. We show that the complexity for the boundedness problem for this UCRPQs fragment is $\Pi^P_2$-complete, and that an equivalent bounded query can be produced in polynomial time whenever possible. When the query turns out to be unbounded, we also study the task of finding an equivalent maximally bounded query, which we show to be feasible in $\Pi^P_2$. As a side result of independent interest stemming from our developments, we study a notion of succinct finite automata and prove that its membership problem is in NP.