1,667 research outputs found
Provenance Circuits for Trees and Treelike Instances (Extended Version)
Query evaluation in monadic second-order logic (MSO) is tractable on trees
and treelike instances, even though it is hard for arbitrary instances. This
tractability result has been extended to several tasks related to query
evaluation, such as counting query results [3] or performing query evaluation
on probabilistic trees [10]. These are two examples of the more general problem
of computing augmented query output, that is referred to as provenance. This
article presents a provenance framework for trees and treelike instances, by
describing a linear-time construction of a circuit provenance representation
for MSO queries. We show how this provenance can be connected to the usual
definitions of semiring provenance on relational instances [20], even though we
compute it in an unusual way, using tree automata; we do so via intrinsic
definitions of provenance for general semirings, independent of the operational
details of query evaluation. We show applications of this provenance to capture
existing counting and probabilistic results on trees and treelike instances,
and give novel consequences for probability evaluation.Comment: 48 pages. Presented at ICALP'1
Answering SPARQL queries modulo RDF Schema with paths
SPARQL is the standard query language for RDF graphs. In its strict
instantiation, it only offers querying according to the RDF semantics and would
thus ignore the semantics of data expressed with respect to (RDF) schemas or
(OWL) ontologies. Several extensions to SPARQL have been proposed to query RDF
data modulo RDFS, i.e., interpreting the query with RDFS semantics and/or
considering external ontologies. We introduce a general framework which allows
for expressing query answering modulo a particular semantics in an homogeneous
way. In this paper, we discuss extensions of SPARQL that use regular
expressions to navigate RDF graphs and may be used to answer queries
considering RDFS semantics. We also consider their embedding as extensions of
SPARQL. These SPARQL extensions are interpreted within the proposed framework
and their drawbacks are presented. In particular, we show that the PSPARQL
query language, a strict extension of SPARQL offering transitive closure,
allows for answering SPARQL queries modulo RDFS graphs with the same complexity
as SPARQL through a simple transformation of the queries. We also consider
languages which, in addition to paths, provide constraints. In particular, we
present and compare nSPARQL and our proposal CPSPARQL. We show that CPSPARQL is
expressive enough to answer full SPARQL queries modulo RDFS. Finally, we
compare the expressiveness and complexity of both nSPARQL and the corresponding
fragment of CPSPARQL, that we call cpSPARQL. We show that both languages have
the same complexity through cpSPARQL, being a proper extension of SPARQL graph
patterns, is more expressive than nSPARQL.Comment: RR-8394; alkhateeb2003
Joining Extractions of Regular Expressions
Regular expressions with capture variables, also known as "regex formulas,"
extract relations of spans (interval positions) from text. These relations can
be further manipulated via Relational Algebra as studied in the context of
document spanners, Fagin et al.'s formal framework for information extraction.
We investigate the complexity of querying text by Conjunctive Queries (CQs) and
Unions of CQs (UCQs) on top of regex formulas. We show that the lower bounds
(NP-completeness and W[1]-hardness) from the relational world also hold in our
setting; in particular, hardness hits already single-character text! Yet, the
upper bounds from the relational world do not carry over. Unlike the relational
world, acyclic CQs, and even gamma-acyclic CQs, are hard to compute. The source
of hardness is that it may be intractable to instantiate the relation defined
by a regex formula, simply because it has an exponential number of tuples. Yet,
we are able to establish general upper bounds. In particular, UCQs can be
evaluated with polynomial delay, provided that every CQ has a bounded number of
atoms (while unions and projection can be arbitrary). Furthermore, UCQ
evaluation is solvable with FPT (Fixed-Parameter Tractable) delay when the
parameter is the size of the UCQ
Formal Verification of Differential Privacy for Interactive Systems
Differential privacy is a promising approach to privacy preserving data
analysis with a well-developed theory for functions. Despite recent work on
implementing systems that aim to provide differential privacy, the problem of
formally verifying that these systems have differential privacy has not been
adequately addressed. This paper presents the first results towards automated
verification of source code for differentially private interactive systems. We
develop a formal probabilistic automaton model of differential privacy for
systems by adapting prior work on differential privacy for functions. The main
technical result of the paper is a sound proof technique based on a form of
probabilistic bisimulation relation for proving that a system modeled as a
probabilistic automaton satisfies differential privacy. The novelty lies in the
way we track quantitative privacy leakage bounds using a relation family
instead of a single relation. We illustrate the proof technique on a
representative automaton motivated by PINQ, an implemented system that is
intended to provide differential privacy. To make our proof technique easier to
apply to realistic systems, we prove a form of refinement theorem and apply it
to show that a refinement of the abstract PINQ automaton also satisfies our
differential privacy definition. Finally, we begin the process of automating
our proof technique by providing an algorithm for mechanically checking a
restricted class of relations from the proof technique.Comment: 65 pages with 1 figur
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