9 research outputs found
Consistent Query Answering for Primary Keys and Conjunctive Queries with Counting
The problem of consistent query answering for primary keys and self-join-free
conjunctive queries has been intensively studied in recent years and is by now
well understood. In this paper, we study an extension of this problem with
counting. The queries we consider count how many times each value occurs in a
designated (possibly composite) column of an answer to a full conjunctive
query. In a setting of database repairs, we adopt the semantics of [Arenas et
al., ICDT 2001] which computes tight lower and upper bounds on these counts,
where the bounds are taken over all repairs. Ariel Fuxman defined in his PhD
thesis a syntactic class of queries, called C_forest, for which this
computation can be done by executing two first-order queries (one for lower
bounds, and one for upper bounds) followed by simple counting steps. We use the
term "parsimonious counting" for this computation. A natural question is
whether C_forest contains all self-join-free conjunctive queries that admit
parsimonious counting. We answer this question negatively. We define a new
syntactic class of queries, called C_parsimony, and prove that it contains all
(and only) self-join-free conjunctive queries that admit parsimonious counting.Comment: 27 pages, 2 figure
Consistent Query Answering for Primary Keys on Rooted Tree Queries
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 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).Comment: To appear in PODS'2