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

For a given set of queries (which are expressions in some query language) $\mathcal{Q}={Q1$, $Q2, \ldots Qk}$ and for another query $Q0$ we say that $\mathcal{Q}$ determines $Q0$ if -- informally speaking -- for every database $\mathbb D$, the information contained in the views $\mathcal{Q}({\mathbb D})$ is sufficient to compute $Q0({\mathbb D})$. Query Determinacy Problem is the problem of deciding, for given $\mathcal{Q}$ and $Q0$, whether $\mathcal{Q}$ determines $Q0$. 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.