Consistent Query Answering for Primary Keys on Rooted Tree Queries

TL;DR

This paper classifies the data complexity of consistent query answering for rooted tree queries with primary key violations, providing a polynomial-time decision procedure based on query homomorphisms and context-free grammars.

Contribution

It extends the classification of CERTAINTY(q) complexity to all rooted tree queries and introduces a novel fixpoint algorithm using context-free grammars.

Findings

CERTAINTY(q) is in FO, NL-hard ∩ LFP, or coNP-complete for rooted tree queries.

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

Extended classification to larger query classes with simple primary keys.

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 subset of the database satisfying the primary key constraints. For a Boolean query q, the problem CERTAINTY(q) takes a database as input, and asks whether or not each repair satisfies q. The computational complexity of CERTAINTY(q) has been established whenever q is a self-join-free Boolean conjunctive query, or a (not necessarily self-join-free) Boolean path query. In this paper, we take one more step towards a general classification for all Boolean conjunctive queries by considering the class of rooted tree queries. In particular, we show that for every rooted tree query q, CERTAINTY(q) is in FO, NL-hard $\cap$ LFP, or coNP-complete, and it is decidable (in polynomial time), given q, which of the three cases applies. We also extend our classification to larger classes of queries with simple primary keys. Our classification criteria rely on query homomorphisms and our polynomial-time fixpoint algorithm is based on a novel use of context-free grammar (CFG).