23 research outputs found
Competences acquisition of university students: Do they match job market's needs?
This paper aims at analyzing the skills and competences acquired by students during their university studies, in order to identify the extent to which they fit into society's labor market demands
On Optimization Modulo Theories, MaxSMT and Sorting Networks
Optimization Modulo Theories (OMT) is an extension of SMT which allows for
finding models that optimize given objectives. (Partial weighted) MaxSMT --or
equivalently OMT with Pseudo-Boolean objective functions, OMT+PB-- is a
very-relevant strict subcase of OMT. We classify existing approaches for MaxSMT
or OMT+PB in two groups: MaxSAT-based approaches exploit the efficiency of
state-of-the-art MAXSAT solvers, but they are specific-purpose and not always
applicable; OMT-based approaches are general-purpose, but they suffer from
intrinsic inefficiencies on MaxSMT/OMT+PB problems.
We identify a major source of such inefficiencies, and we address it by
enhancing OMT by means of bidirectional sorting networks. We implemented this
idea on top of the OptiMathSAT OMT solver. We run an extensive empirical
evaluation on a variety of problems, comparing MaxSAT-based and OMT-based
techniques, with and without sorting networks, implemented on top of
OptiMathSAT and {\nu}Z. The results support the effectiveness of this idea, and
provide interesting insights about the different approaches.Comment: 17 pages, submitted at Tacas 1
Generalized Totalizer Encoding for Pseudo-Boolean Constraints
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are
used to model many real-world problems. A common approach to solve these
constraints is to encode them into a SAT formula. The runtime of the SAT solver
on such formula is sensitive to the manner in which the given pseudo-Boolean
constraints are encoded. In this paper, we propose generalized Totalizer
encoding (GTE), which is an arc-consistency preserving extension of the
Totalizer encoding to pseudo-Boolean constraints. Unlike some other encodings,
the number of auxiliary variables required for GTE does not depend on the
magnitudes of the coefficients. Instead, it depends on the number of distinct
combinations of these coefficients. We show the superiority of GTE with respect
to other encodings when large pseudo-Boolean constraints have low number of
distinct coefficients. Our experimental results also show that GTE remains
competitive even when the pseudo-Boolean constraints do not have this
characteristic.Comment: 10 pages, 2 figures, 2 tables. To be published in 21st International
Conference on Principles and Practice of Constraint Programming 201
On Solving Word Equations Using SAT
We present Woorpje, a string solver for bounded word equations (i.e.,
equations where the length of each variable is upper bounded by a given
integer). Our algorithm works by reformulating the satisfiability of bounded
word equations as a reachability problem for nondeterministic finite automata,
and then carefully encoding this as a propositional satisfiability problem,
which we then solve using the well-known Glucose SAT-solver. This approach has
the advantage of allowing for the natural inclusion of additional linear length
constraints. Our solver obtains reliable and competitive results and,
remarkably, discovered several cases where state-of-the-art solvers exhibit a
faulty behaviour
Automatic Detection of At-Most-One and Exactly-One Relations for Improved SAT Encodings of Pseudo-Boolean Constraints
Pseudo-Boolean (PB) constraints often have a critical role in constraint satisfaction and optimisation problems. Encoding PB constraints to SAT has proven to be an efficient approach in many applications, however care must be taken to encode them compactly and with good propagation properties. It has been shown that at-most-one (AMO) and exactly-one (EO) relations over subsets of the variables can be exploited in various encodings of PB constraints, improving their compactness and solving performance. In this paper we detect AMO and EO relations completely automatically and exploit them to improve SAT encodings that are based on Multi-Valued Decision Diagrams (MDDs). Our experiments show substantial reductions in encoding size and dramatic improvements in solving time thanks to automatic AMO and EO detection
Ultrametric spaces of branches on arborescent singularities
Let be a normal complex analytic surface singularity. We say that is
arborescent if the dual graph of any resolution of it is a tree. Whenever
are distinct branches on , we denote by their intersection
number in the sense of Mumford. If is a fixed branch, we define when and
otherwise. We generalize a theorem of P{\l}oski concerning smooth germs of
surfaces, by proving that whenever is arborescent, then is an
ultrametric on the set of branches of different from . We compute the
maximum of , which gives an analog of a theorem of Teissier. We show that
encodes topological information about the structure of the embedded
resolutions of any finite set of branches. This generalizes a theorem of Favre
and Jonsson concerning the case when both and are smooth. We generalize
also from smooth germs to arbitrary arborescent ones their valuative
interpretation of the dual trees of the resolutions of . Our proofs are
based in an essential way on a determinantal identity of Eisenbud and Neumann.Comment: 37 pages, 16 figures. Compared to the first version on Arxiv, il has
a new section 4.3, accompanied by 2 new figures. Several passages were
clarified and the typos discovered in the meantime were correcte
On Tackling the Limits of Resolution in SAT Solving
The practical success of Boolean Satisfiability (SAT) solvers stems from the
CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a
propositional proof complexity perspective, CDCL is no more powerful than the
resolution proof system, for which many hard examples exist. This paper
proposes a new problem transformation, which enables reducing the decision
problem for formulas in conjunctive normal form (CNF) to the problem of solving
maximum satisfiability over Horn formulas. Given the new transformation, the
paper proves a polynomial bound on the number of MaxSAT resolution steps for
pigeonhole formulas. This result is in clear contrast with earlier results on
the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper
also establishes the same polynomial bound in the case of modern core-guided
MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard
for CDCL SAT solvers, show that these can be efficiently solved with modern
MaxSAT solvers
Exploiting short supports for improved encoding of arbitrary constraints into SAT
Encoding to SAT and applying a highly efficient modern SAT solver is an increasingly popular method of solving finite-domain constraint problems. In this paper we study encodings of arbitrary constraints where unit propagation on the encoding provides strong reasoning. Specifically, unit propagation on the encoding simulates generalised arc consistency on the original constraint. To create compact and efficient encodings we use the concept of short support. Short support has been successfully applied to create efficient propagation algorithms for arbitrary constraints. A short support of a constraint is similar to a satisfying tuple however a short support is not required to assign every variable in scope. Some variables are left free to take any value. In some cases a short support representation is smaller than the table of satisfying tuples by an exponential factor. We present two encodings based on short supports and evaluate them on a set of benchmark problems, demonstrating a substantial improvement over the state of the art
Textos sobre educación universitaria: la docencia de la estadística (2017)
Esta publicación recopila las distintas contribuciones del Grupo de Innovación Docente Consolidado “ANDES - Análisis de Datos en Economía y Empresa” sobre la innovación docente en el amplio universo del análisis de datos. Esta obra tiene como objetivo hacer llegar a los docentes universitarios y a los interesados en la docencia universitaria la investigación y la innovación que se producen en este ámbito. El Grupo de Innovación Docente Consolidado “ANDES” tiene como objetivos estudiar, analizar, ajustar y movilizar los recursos y acciones necesarias para mejorar la docencia de la Estadística y otras asignaturas de análisis de datos, que se dirigen a estudiantes de diferentes Grados, como Estadística, ADE, Economía, etc. Fundamentalmente, el trabajo de innovación docente se focaliza en asignaturas obligatorias y troncales de los Grados mencionados.Este texto ha sido llevado a cabo en el marco del proyecto 2013PID-UB/004. Agradecemos a la Universitat de Barcelona su apoyo y financiación.Projecte 2013PID-UB/00