14,533 research outputs found
Efficient Parallel Path Checking for Linear-Time Temporal Logic With Past and Bounds
Path checking, the special case of the model checking problem where the model
under consideration is a single path, plays an important role in monitoring,
testing, and verification. We prove that for linear-time temporal logic (LTL),
path checking can be efficiently parallelized. In addition to the core logic,
we consider the extensions of LTL with bounded-future (BLTL) and past-time
(LTL+Past) operators. Even though both extensions improve the succinctness of
the logic exponentially, path checking remains efficiently parallelizable: Our
algorithm for LTL, LTL+Past, and BLTL+Past is in AC^1(logDCFL) \subseteq NC
Faster Query Answering in Probabilistic Databases using Read-Once Functions
A boolean expression is in read-once form if each of its variables appears
exactly once. When the variables denote independent events in a probability
space, the probability of the event denoted by the whole expression in
read-once form can be computed in polynomial time (whereas the general problem
for arbitrary expressions is #P-complete). Known approaches to checking
read-once property seem to require putting these expressions in disjunctive
normal form. In this paper, we tell a better story for a large subclass of
boolean event expressions: those that are generated by conjunctive queries
without self-joins and on tuple-independent probabilistic databases. We first
show that given a tuple-independent representation and the provenance graph of
an SPJ query plan without self-joins, we can, without using the DNF of a result
event expression, efficiently compute its co-occurrence graph. From this, the
read-once form can already, if it exists, be computed efficiently using
existing techniques. Our second and key contribution is a complete, efficient,
and simple to implement algorithm for computing the read-once forms (whenever
they exist) directly, using a new concept, that of co-table graph, which can be
significantly smaller than the co-occurrence graph.Comment: Accepted in ICDT 201
Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays
The goal of this paper is to introduce a new method in computer-aided
geometry of solid modeling. We put forth a novel algebraic technique to
evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with
regularized operators of union, intersection, and difference, i.e., any CSG
tree. The result is obtained in three steps: first, by computing an independent
set of generators for the d-space partition induced by the input; then, by
reducing the solid expression to an equivalent logical formula between Boolean
terms made by zeros and ones; and, finally, by evaluating this expression using
bitwise operators. This method is implemented in Julia using sparse arrays. The
computational evaluation of every possible solid expression, usually denoted as
CSG (Constructive Solid Geometry), is reduced to an equivalent logical
expression of a finite set algebra over the cells of a space partition, and
solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig
A SAT-based System for Consistent Query Answering
An inconsistent database is a database that violates one or more integrity
constraints, such as functional dependencies. Consistent Query Answering is a
rigorous and principled approach to the semantics of queries posed against
inconsistent databases. The consistent answers to a query on an inconsistent
database is the intersection of the answers to the query on every repair, i.e.,
on every consistent database that differs from the given inconsistent one in a
minimal way. Computing the consistent answers of a fixed conjunctive query on a
given inconsistent database can be a coNP-hard problem, even though every fixed
conjunctive query is efficiently computable on a given consistent database.
We designed, implemented, and evaluated CAvSAT, a SAT-based system for
consistent query answering. CAvSAT leverages a set of natural reductions from
the complement of consistent query answering to SAT and to Weighted MaxSAT. The
system is capable of handling unions of conjunctive queries and arbitrary
denial constraints, which include functional dependencies as a special case. We
report results from experiments evaluating CAvSAT on both synthetic and
real-world databases. These results provide evidence that a SAT-based approach
can give rise to a comprehensive and scalable system for consistent query
answering.Comment: 25 pages including appendix, to appear in the 22nd International
Conference on Theory and Applications of Satisfiability Testin
QuickCSG: Fast Arbitrary Boolean Combinations of N Solids
QuickCSG computes the result for general N-polyhedron boolean expressions
without an intermediate tree of solids. We propose a vertex-centric view of the
problem, which simplifies the identification of final geometric contributions,
and facilitates its spatial decomposition. The problem is then cast in a single
KD-tree exploration, geared toward the result by early pruning of any region of
space not contributing to the final surface. We assume strong regularity
properties on the input meshes and that they are in general position. This
simplifying assumption, in combination with our vertex-centric approach,
improves the speed of the approach. Complemented with a task-stealing
parallelization, the algorithm achieves breakthrough performance, one to two
orders of magnitude speedups with respect to state-of-the-art CPU algorithms,
on boolean operations over two to dozens of polyhedra. The algorithm also
outperforms GPU implementations with approximate discretizations, while
producing an output without redundant facets. Despite the restrictive
assumptions on the input, we show the usefulness of QuickCSG for applications
with large CSG problems and strong temporal constraints, e.g. modeling for 3D
printers, reconstruction from visual hulls and collision detection
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