Decidability of Equivalence of Aggregate Count-Distinct Queries

TL;DR

This paper proves that determining the equivalence of count-distinct aggregate queries is decidable within the third level of the Polynomial hierarchy, introducing new concepts like query cores and their isomorphisms.

Contribution

It extends classical query equivalence notions to count-distinct queries, establishing decidability and introducing new notions to capture their behavior.

Findings

Equivalence of count-distinct queries is decidable.

Introduction of query cores and their isomorphism as a criterion.

A relaxation condition for equivalence based on a new notion.

Abstract

We address the problem of equivalence of count-distinct aggregate queries, prove that the problem is decidable, and can be decided in the third level of Polynomial hierarchy. We introduce the notion of core for conjunctive queries with comparisons as an extension of the classical notion for relational queries, and prove that the existence of isomorphism among cores of queries is a sufficient and necessary condition for equivalence of conjunctive queries with comparisons similar to the classical relational setting. However, it is not a necessary condition for equivalence of count-distinct queries. We introduce a relaxation of this condition based on a new notion, which is a potentially new query equivalent to the initial query, introduced to capture the behavior of count-distinct operator.