44 research outputs found
Eliminating Recursion from Monadic Datalog Programs on Trees
We study the problem of eliminating recursion from monadic datalog programs
on trees with an infinite set of labels. We show that the boundedness problem,
i.e., determining whether a datalog program is equivalent to some nonrecursive
one is undecidable but the decidability is regained if the descendant relation
is disallowed. Under similar restrictions we obtain decidability of the problem
of equivalence to a given nonrecursive program. We investigate the connection
between these two problems in more detail
Queries with Guarded Negation (full version)
A well-established and fundamental insight in database theory is that
negation (also known as complementation) tends to make queries difficult to
process and difficult to reason about. Many basic problems are decidable and
admit practical algorithms in the case of unions of conjunctive queries, but
become difficult or even undecidable when queries are allowed to contain
negation. Inspired by recent results in finite model theory, we consider a
restricted form of negation, guarded negation. We introduce a fragment of SQL,
called GN-SQL, as well as a fragment of Datalog with stratified negation,
called GN-Datalog, that allow only guarded negation, and we show that these
query languages are computationally well behaved, in terms of testing query
containment, query evaluation, open-world query answering, and boundedness.
GN-SQL and GN-Datalog subsume a number of well known query languages and
constraint languages, such as unions of conjunctive queries, monadic Datalog,
and frontier-guarded tgds. In addition, an analysis of standard benchmark
workloads shows that most usage of negation in SQL in practice is guarded
negation
The Complexity of Datalog on Linear Orders
We study the program complexity of datalog on both finite and infinite linear
orders. Our main result states that on all linear orders with at least two
elements, the nonemptiness problem for datalog is EXPTIME-complete. While
containment of the nonemptiness problem in EXPTIME is known for finite linear
orders and actually for arbitrary finite structures, it is not obvious for
infinite linear orders. It sharply contrasts the situation on other infinite
structures; for example, the datalog nonemptiness problem on an infinite
successor structure is undecidable. We extend our upper bound results to
infinite linear orders with constants.
As an application, we show that the datalog nonemptiness problem on Allen's
interval algebra is EXPTIME-complete.Comment: 21 page
Evaluating Datalog via Tree Automata and Cycluits
We investigate parameterizations of both database instances and queries that
make query evaluation fixed-parameter tractable in combined complexity. We show
that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog)
enjoys bilinear-time evaluation on structures of bounded treewidth for programs
of bounded rule size. Such programs capture in particular conjunctive queries
with simplicial decompositions of bounded width, guarded negation fragment
queries of bounded CQ-rank, or two-way regular path queries. Our result is
shown by translating to alternating two-way automata, whose semantics is
defined via cyclic provenance circuits (cycluits) that can be tractably
evaluated.Comment: 56 pages, 63 references. Journal version of "Combined Tractability of
Query Evaluation via Tree Automata and Cycluits (Extended Version)" at
arXiv:1612.04203. Up to the stylesheet, page/environment numbering, and
possible minor publisher-induced changes, this is the exact content of the
journal paper that will appear in Theory of Computing Systems. Update wrt
version 1: latest reviewer feedbac
Regular Queries on Graph Databases
Graph databases are currently one of the most popular paradigms for storing data. One of the key conceptual differences between graph and relational databases is the focus on navigational queries that ask whether some nodes are connected by paths satisfying certain restrictions. This focus has driven the definition of several different query languages and the subsequent study of their fundamental properties.
We define the graph query language of Regular Queries, which is a natural extension of unions of conjunctive 2-way regular path queries (UC2RPQs) and unions of conjunctive nested 2-way regular path queries (UCN2RPQs). Regular queries allow expressing complex regular patterns between nodes. We formalize regular queries as nonrecursive Datalog programs with transitive closure rules. This language has been previously considered, but its algorithmic properties are not well understood.
Our main contribution is to show elementary tight bounds for the containment problem for regular queries. Specifically, we show that this problem is 2EXPSPACE-complete. For all extensions of regular queries known to date, the containment problem turns out to be non-elementary. Together with the fact that evaluating regular queries is not harder than evaluating UCN2RPQs, our results show that regular queries achieve a good balance between expressiveness and complexity, and constitute a well-behaved class that deserves further investigation
Querying Schemas With Access Restrictions
We study verification of systems whose transitions consist of accesses to a
Web-based data-source. An access is a lookup on a relation within a relational
database, fixing values for a set of positions in the relation. For example, a
transition can represent access to a Web form, where the user is restricted to
filling in values for a particular set of fields. We look at verifying
properties of a schema describing the possible accesses of such a system. We
present a language where one can describe the properties of an access path, and
also specify additional restrictions on accesses that are enforced by the
schema. Our main property language, AccLTL, is based on a first-order extension
of linear-time temporal logic, interpreting access paths as sequences of
relational structures. We also present a lower-level automaton model,
Aautomata, which AccLTL specifications can compile into. We show that AccLTL
and A-automata can express static analysis problems related to "querying with
limited access patterns" that have been studied in the database literature in
the past, such as whether an access is relevant to answering a query, and
whether two queries are equivalent in the accessible data they can return. We
prove decidability and complexity results for several restrictions and variants
of AccLTL, and explain which properties of paths can be expressed in each
restriction.Comment: VLDB201