Scalable Parallel Numerical CSP Solver

We present a parallel solver for numerical constraint satisfaction problems (NCSPs) that can scale on a number of cores. Our proposed method runs worker solvers on the available cores and simultaneously the workers cooperate for the search space distribution and balancing. In the experiments, we attained up to 119-fold speedup using 256 cores of a parallel computer.Comment: The final publication is available at Springe

Introduction aux contraintes d'intervalles; application à l'estimation à erreurs bornées

à Biarritz (France) du 15/11 au 16/11/2001Journées S3P "Simulation de Produits, de Procédés et de Processus industriels"Dans cet article, nous allons décrire le formalisme des contraintes d'intervalles appliquées au problème de l'estimation d'une somme de trois exponentielles dans un contexte à erreurs bornées. Les outils dédiés aux contraintes constituent une alternative aux méthodes d'optimisation classiques. Ils accélèrent la convergence, et garantissent des solutions fiables

Hull Consistency Under Monotonicity

International audienceWe prove that hull consistency for a system of equations or inequalities can be achieved in polynomial time providing that the underlying functions are monotone with respect to each variable. This result holds including when variables have multiple occurrences in the expressions of the functions, which is usually a pitfall for interval-based contractors. For a given constraint, an optimal contractor can thus be enforced quickly under monotonicity and the practical significance of this theoretical result is illustrated on a simple example

Real Algebraic Strategies for MetiTarski Proofs

Abstract. MetiTarski [1] is an automatic theorem prover that can prove inequalities involving sin, cos, exp, ln, etc. During its proof search, it generates a series of subproblems in nonlinear polynomial real arithmetic which are reduced to true or false using a decision procedure for the theory of real closed fields (RCF). These calls are often a bottleneck: RCF is fundamentally infeasible. However, by studying these subproblems, we can design specialised variants of RCF decision procedures that run faster and improve MetiTarski’s performance.

Symmetry breaking in numeric constraint problems

Symmetry-breaking constraints in the form of inequalities between variables have been proposed for a few kind of solution symmetries in numeric CSPs. We show that, for the variable symmetries among those, the proposed inequalities are but a specific case of a relaxation of the well-known LEX constraints extensively used for discrete CSPs. We discuss the merits of this relaxation and present experimental evidences of its practical interest.Postprint (author’s final draft

Computation in Real Closed Infinitesimal and Transcendental Extensions of the Rationals.

Abstract. Recent applications of decision procedures for nonlinear real arithmetic (the theory of real closed fields, or RCF) have presented a need for reasoning not only with polynomials but also with transcendental constants and infinitesimals. In full generality, the algebraic setting for this reasoning consists of real closed transcendental and infinitesimal extensions of the rational numbers. We present a library for computing over these extensions. This library contains many contributions, including a novel combination of Thom’s Lemma and interval arithmetic for representing roots, and provides all core machinery required for building RCF decision procedures. We describe the abstract algebraic setting for computing with such field extensions, present our concrete algorithms and optimizations, and illustrate the library on a collection of examples. 1 Overview and Related Work Decision methods for nonlinear real arithmetic are essential to the formal verification of cyber-physical systems and formalized mathematics. Classically, thes

Horner\u27s Rule for Interval Evaluation Revisited

Interval arithmetic can be used to enclose the range of a real function over a domain. However, due to some weak properties of interval arithmetic, a computed interval can be much larger than the exact range. This phenomenon is called dependency problem. In this paper, Horner\u27s rule for polynomial interval evaluation is revisited. We introduce a new factorization scheme based on well-known symbolic identities in order to handle the dependency problem of interval arithmetic. The experimental results show an improvement of 25% of the width of computed intervals with respect to Horner\u27s rule