2,690 research outputs found
Tractable Combinations of Global Constraints
We study the complexity of constraint satisfaction problems involving global
constraints, i.e., special-purpose constraints provided by a solver and
represented implicitly by a parametrised algorithm. Such constraints are widely
used; indeed, they are one of the key reasons for the success of constraint
programming in solving real-world problems.
Previous work has focused on the development of efficient propagators for
individual constraints. In this paper, we identify a new tractable class of
constraint problems involving global constraints of unbounded arity. To do so,
we combine structural restrictions with the observation that some important
types of global constraint do not distinguish between large classes of
equivalent solutions.Comment: To appear in proceedings of CP'13, LNCS 8124. arXiv admin note: text
overlap with arXiv:1307.179
Implementing Non-Linear Constraints with Cooperative Solvers
We investigate the use of cooperation between solvers in the scheme of constraint logic programming languages over the domain of non-linear polynomial constraints. Instead of using a general and often inefficient decision procedure we propose a new approach for handling these constraints by cooperating specialised solvers. Our approach requires the design of a client/server architecture to enable communication between the various components. The main modules are a linear solver, a non-linear solver, a constraint manager, a communication protocol component and an answer processor module. This work is motivated by the need for a declarative system for robot motion planning and geometric problem solving. We have implemented a prototype called \groak %({\bf \sf C\raisebox{.2ex}o}nstraint {\bf \sf S}ystem {\bf \sf %A}r{\bf \sf \raisebox{.2ex}c}hitecture) (\textbf{\textsf C}\raisebox{.2ex}{\textbf{\textsfo}}nstraint \textbf{\textsfS}ystem \textbf{\textsfA}r\raisebox{.2ex}{\textbf{\textsfc}}hit- ecture) to validate our approach using cooperating solvers for non-linear constraints over the real numbers. Our language is illustrated by an example that also shows the advantages of cooperation
Scalable Coordinated Beamforming for Dense Wireless Cooperative Networks
To meet the ever growing demand for both high throughput and uniform coverage
in future wireless networks, dense network deployment will be ubiquitous, for
which co- operation among the access points is critical. Considering the
computational complexity of designing coordinated beamformers for dense
networks, low-complexity and suboptimal precoding strategies are often adopted.
However, it is not clear how much performance loss will be caused. To enable
optimal coordinated beamforming, in this paper, we propose a framework to
design a scalable beamforming algorithm based on the alternative direction
method of multipliers (ADMM) method. Specifically, we first propose to apply
the matrix stuffing technique to transform the original optimization problem to
an equivalent ADMM-compliant problem, which is much more efficient than the
widely-used modeling framework CVX. We will then propose to use the ADMM
algorithm, a.k.a. the operator splitting method, to solve the transformed
ADMM-compliant problem efficiently. In particular, the subproblems of the ADMM
algorithm at each iteration can be solved with closed-forms and in parallel.
Simulation results show that the proposed techniques can result in significant
computational efficiency compared to the state- of-the-art interior-point
solvers. Furthermore, the simulation results demonstrate that the optimal
coordinated beamforming can significantly improve the system performance
compared to sub-optimal zero forcing beamforming
ILP Modulo Data
The vast quantity of data generated and captured every day has led to a
pressing need for tools and processes to organize, analyze and interrelate this
data. Automated reasoning and optimization tools with inherent support for data
could enable advancements in a variety of contexts, from data-backed decision
making to data-intensive scientific research. To this end, we introduce a
decidable logic aimed at database analysis. Our logic extends quantifier-free
Linear Integer Arithmetic with operators from Relational Algebra, like
selection and cross product. We provide a scalable decision procedure that is
based on the BC(T) architecture for ILP Modulo Theories. Our decision procedure
makes use of database techniques. We also experimentally evaluate our approach,
and discuss potential applications.Comment: FMCAD 2014 final version plus proof
Propagators and Solvers for the Algebra of Modular Systems
To appear in the proceedings of LPAR 21.
Solving complex problems can involve non-trivial combinations of distinct
knowledge bases and problem solvers. The Algebra of Modular Systems is a
knowledge representation framework that provides a method for formally
specifying such systems in purely semantic terms. Formally, an expression of
the algebra defines a class of structures. Many expressive formalism used in
practice solve the model expansion task, where a structure is given on the
input and an expansion of this structure in the defined class of structures is
searched (this practice overcomes the common undecidability problem for
expressive logics). In this paper, we construct a solver for the model
expansion task for a complex modular systems from an expression in the algebra
and black-box propagators or solvers for the primitive modules. To this end, we
define a general notion of propagators equipped with an explanation mechanism,
an extension of the alge- bra to propagators, and a lazy conflict-driven
learning algorithm. The result is a framework for seamlessly combining solving
technology from different domains to produce a solver for a combined system.Comment: To appear in the proceedings of LPAR 2
Efficient Interpolant Generation in Satisfiability Modulo Theories
The problem of computing Craig Interpolants for propositional (SAT) formulas has recently received a lot of interest, mainly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many interesting verification problems, which can be more naturally addressed in the framework of Satisfiability Modulo Theories, SMT. Although {some} works have addressed the topic of generating interpolants in SMT, the techniques and tools that are currently available have some limitations, and their performance still does not exploit the full power of current state-of-the-art SMT solvers. In this paper we try to close this gap. We present several techniques for interpolant generation in SMT which overcome the limitations of the current generators mentioned above, and which take full advantage of state-of-the-art SMT technology. These novel techniques can lead to substantial performance improvements wrt. the currently available tools. We support our claims with an extensive experimental evaluation of our implementation of the proposed techniques in the MathSAT SMT solver
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