Red Spider Meets a Rainworm: Conjunctive Query Finite Determinacy Is Undecidable

TL;DR

This paper proves that the problem of determining whether a set of conjunctive queries finitely determines another is undecidable, resolving a long-standing open problem in database theory using advanced techniques.

Contribution

It establishes the undecidability of the Conjunctive Query Finite Determinacy Problem and introduces a specific instance illustrating finite but not full determinacy.

Findings

Decidability of the problem is impossible in general.

Existence of a specific query instance with finite but not complete determinacy.

No FO-rewriting exists for certain finitely determined queries.

Abstract

We solve a well known and long-standing open problem in database theory, proving that Conjunctive Query Finite Determinacy Problem is undecidable. The technique we use builds on the top of our Red Spider method which we developed in our paper [GM15] to show undecidability of the same problem in the "unrestricted case" -- when database instances are allowed to be infinite. We also show a specific instance $Q_0$, ${\cal Q}= \{Q_1, Q_2, \ldots Q_k\}$ such that the set $\cal Q$ of CQs does not determine CQ $Q_0$ but finitely determines it. Finally, we claim that while $Q_0$ is finitely determined by $\cal Q$, there is no FO-rewriting of $Q_0$, with respect to $\cal Q$, and we outline a proof of this claim