Consistent Query Answering for Primary Keys on Path Queries

TL;DR

This paper analyzes the data complexity of consistent query answering for databases with primary key violations, revealing a four-way complexity classification for path queries when self-joins are permitted.

Contribution

It extends previous work by establishing a tetrachotomy classification for the complexity of CQA on path queries with self-joins, and provides a polynomial-time method to determine the complexity class.

Findings

Complexity of CERTAINTY(q) for path queries with self-joins falls into four classes.

Decidable in polynomial time which complexity class applies to a given query.

Provides a comprehensive classification extending known results for self-join-free queries.

Abstract

We study the data complexity of consistent query answering (CQA) on databases that may violate the primary key constraints. A repair is a maximal consistent subset of the database. For a Boolean query $q$, the problem $\mathsf{CERTAINTY}(q)$ takes a database as input, and asks whether or not each repair satisfies $q$. It is known that for any self-join-free Boolean conjunctive query $q$, $\mathsf{CERTAINTY}(q)$ is in $\mathbf{FO}$, $\mathbf{LSPACE}$-complete, or $\mathbf{coNP}$-complete. In particular, $\mathsf{CERTAINTY}(q)$ is in $\mathbf{FO}$ for any self-join-free Boolean path query $q$. In this paper, we show that if self-joins are allowed, the complexity of $\mathsf{CERTAINTY}(q)$ for Boolean path queries $q$ exhibits a tetrachotomy between $\mathbf{FO}$, $\mathbf{NL}$-complete, $\mathbf{PTIME}$-complete, and $\mathbf{coNP}$-complete. Moreover, it is decidable, in polynomial time in the size of the query~$q$, which of the four cases applies.