Consistent Query Answering for Primary Keys in Logspace

TL;DR

This paper classifies the complexity of consistent query answering with primary key violations, showing a dichotomy between logspace expressibility and coNP-completeness for self-join-free conjunctive queries.

Contribution

It refines previous complexity classifications by establishing a dichotomy between symmetric stratified Datalog expressibility and coNP-completeness, especially highlighting the practical case of foreign key joins.

Findings

CERTAINTY(q) is either in L or coNP-complete.

CERTAINTY(q) is in L for foreign key join queries.

Provides a practical complexity classification for common database queries.

Abstract

We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean query q, CERTAINTY(q) is the problem that takes a database as input and asks whether q evaluates to true on every repair. In [KW17], the authors show that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either in P or coNP-complete, and it is decidable which of the two cases applies. In this paper, we sharpen this result by showing that for every self-join-free Boolean conjunctive query q, the problem CERTAINTY(q) is either expressible in symmetric stratified Datalog or coNP-complete. Since symmetric stratified Datalog is in L, we thus obtain a complexity-theoretic dichotomy between L and coNP-complete. Another new finding of practical importance is that CERTAINTY(q) is on the logspace side of the dichotomy for queries q where all join conditions express foreign-to-primary key matches, which is undoubtedly the most common type of join condition.