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arXiv · 2609.03908

Property Testing for Recursive Query Languages

Isolde Adler·Carsten Lutz·Quentin Manière·Marcin Przybyłko·Lukas Schulze
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Abstract

In the context of database querying, property testing provides a framework for testing query answers with high confidence while inspecting only a sublinear part of the database, through completion queries and size queries. A fundamental result of Chen and Yoshida (2019) states that non-satisfaction of a Boolean conjunctive query $q$ is testable with a constant number of such queries and one-sided error if and only if $q$ is equivalent to an $\alpha$-acyclic query. In this article, we initiate the study of property testing for recursive query languages, focusing on two-way regular path queries (2RPQs) and monadic Datalog. One of our main results is positive: non-answers to any 2RPQ are constant query testable with one-sided error. We extend this slightly to a certain class of monadic Datalog programs in which recursion is restricted to be linear and rule bodies must be $\alpha$-acyclic. Turning towards unrestricted monadic Datalog, we next show that if a monadic Datalog program $\Pi$ is not equivalent to an $\alpha$-acyclic program, then falsity of $\Pi$ is not constant query testable with one-sided error. This is under the assumption that all rule-bodies are self-join free. We leave open the case of monadic Datalog programs with $\alpha$-acyclic rule bodies that are not restricted to linear recursion, but observe as a first step that there exist $\alpha$-acyclic programs that are mildly non-linear and constant query testable with one-sided error.

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Isolde Adler, Carsten Lutz, Quentin Manière, Marcin Przybyłko, Lukas Schulze. 2026-09-03. Property Testing for Recursive Query Languages. https://arxiv.org/abs/2609.03908

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