5,204 research outputs found
Solving equations in the relational algebra
Enumerating all solutions of a relational algebra equation is a natural and
powerful operation which, when added as a query language primitive to the
nested relational algebra, yields a query language for nested relational
databases, equivalent to the well-known powerset algebra. We study
\emph{sparse} equations, which are equations with at most polynomially many
solutions. We look at their complexity, and compare their expressive power with
that of similar notions in the powerset algebra.Comment: Minor revision, accepted for publication in SIAM Journal on Computin
Knowledge Compilation of Logic Programs Using Approximation Fixpoint Theory
To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of
ICLP 2015
Recent advances in knowledge compilation introduced techniques to compile
\emph{positive} logic programs into propositional logic, essentially exploiting
the constructive nature of the least fixpoint computation. This approach has
several advantages over existing approaches: it maintains logical equivalence,
does not require (expensive) loop-breaking preprocessing or the introduction of
auxiliary variables, and significantly outperforms existing algorithms.
Unfortunately, this technique is limited to \emph{negation-free} programs. In
this paper, we show how to extend it to general logic programs under the
well-founded semantics.
We develop our work in approximation fixpoint theory, an algebraical
framework that unifies semantics of different logics. As such, our algebraical
results are also applicable to autoepistemic logic, default logic and abstract
dialectical frameworks
Evaluating geometric queries using few arithmetic operations
Let \cp:=(P_1,...,P_s) be a given family of -variate polynomials with
integer coefficients and suppose that the degrees and logarithmic heights of
these polynomials are bounded by and , respectively. Suppose furthermore
that for each the polynomial can be evaluated using
arithmetic operations (additions, subtractions, multiplications and the
constants 0 and 1). Assume that the family \cp is in a suitable sense
\emph{generic}. We construct a database , supported by an algebraic
computation tree, such that for each the query for the signs of
can be answered using h d^{\cO(n^2)} comparisons and
arithmetic operations between real numbers. The arithmetic-geometric tools
developed for the construction of are then employed to exhibit example
classes of systems of polynomial equations in unknowns whose
consistency may be checked using only few arithmetic operations, admitting
however an exponential number of comparisons
Resource Control for Synchronous Cooperative Threads
We develop new methods to statically bound the resources needed for the
execution of systems of concurrent, interactive threads. Our study is concerned
with a \emph{synchronous} model of interaction based on cooperative threads
whose execution proceeds in synchronous rounds called instants. Our
contribution is a system of compositional static analyses to guarantee that
each instant terminates and to bound the size of the values computed by the
system as a function of the size of its parameters at the beginning of the
instant. Our method generalises an approach designed for first-order functional
languages that relies on a combination of standard termination techniques for
term rewriting systems and an analysis of the size of the computed values based
on the notion of quasi-interpretation. We show that these two methods can be
combined to obtain an explicit polynomial bound on the resources needed for the
execution of the system during an instant. As a second contribution, we
introduce a virtual machine and a related bytecode thus producing a precise
description of the resources needed for the execution of a system. In this
context, we present a suitable control flow analysis that allows to formulte
the static analyses for resource control at byte code level
On the Solution of Linear Programming Problems in the Age of Big Data
The Big Data phenomenon has spawned large-scale linear programming problems.
In many cases, these problems are non-stationary. In this paper, we describe a
new scalable algorithm called NSLP for solving high-dimensional, non-stationary
linear programming problems on modern cluster computing systems. The algorithm
consists of two phases: Quest and Targeting. The Quest phase calculates a
solution of the system of inequalities defining the constraint system of the
linear programming problem under the condition of dynamic changes in input
data. To this end, the apparatus of Fejer mappings is used. The Targeting phase
forms a special system of points having the shape of an n-dimensional
axisymmetric cross. The cross moves in the n-dimensional space in such a way
that the solution of the linear programming problem is located all the time in
an "-vicinity of the central point of the cross.Comment: Parallel Computational Technologies - 11th International Conference,
PCT 2017, Kazan, Russia, April 3-7, 2017, Proceedings (to be published in
Communications in Computer and Information Science, vol. 753
- …