Can One Escape Red Chains? Regular Path Queries Determinacy is Undecidable

TL;DR

This paper proves that determining whether a set of regular path queries can infer another query's result in graph databases is undecidable, highlighting fundamental limits in query analysis.

Contribution

It establishes the undecidability of the query determinacy problem specifically for regular path queries, a key language in graph database theory.

Findings

Query determinacy is undecidable for regular path queries.

The result resolves a problem posed in 2002.

Highlights limits of query analysis in graph databases.

Abstract

For a given set of queries (which are expressions in some query language) $\mathcal{Q}=\{Q_1$, $Q_2, \ldots Q_k\}$ and for another query $Q_0$ we say that $\mathcal{Q}$ determines $Q_0$ if -- informally speaking -- for every database $\mathbb D$, the information contained in the views $\mathcal{Q}({\mathbb D})$ is sufficient to compute $Q_0({\mathbb D})$. Query Determinacy Problem is the problem of deciding, for given $\mathcal{Q}$ and $Q_0$, whether $\mathcal{Q}$ determines $Q_0$. Many versions of this problem, for different query languages, were studied in database theory. In this paper we solve a problem stated in [CGLV02] and show that Query Determinacy Problem is undecidable for the Regular Path Queries -- the paradigmatic query language of graph databases.