Generalizing Consistency and other Constraint Properties to Quantified Constraints

Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the usual notion of solution inappropriate. As a consequence, basic properties of Constraint Satisfaction Problems (CSP), such as consistency or substitutability, are not completely understood in the quantified case. These properties are important because they are the basis of most of the reasoning methods used to solve classical (existentially quantified) constraints, and one would like to benefit from similar reasoning methods in the resolution of quantified constraints. In this paper, we show that most of the properties that are used by solvers for CSP can be generalized to quantified CSP. This requires a re-thinking of a number of basic concepts; in particular, we propose a notion of outcome that generalizes the classical notion of solution and on which all definitions are based. We propose a systematic study of the relations which hold between these properties, as well as complexity results regarding the decision of these properties. Finally, and since these problems are typically intractable, we generalize the approach used in CSP and propose weaker, easier to check notions based on locality, which allow to detect these properties incompletely but in polynomial time

Nickel sulphide: new results to optimise the heat soak test for thermally toughened building glasses

The spontaneous failure of tempered facade glazings has been known as a security and reputation problem of these beautiful parts of the surface of modern buildings since the late fifties. By kinetic investigations on synthetic nickel sulphides and by statistical analysis of the breakage of heat soak test ovens it is shown that this problem can be solved. If the test is done in a right and careful way, at temperatures of (290 ± 10) °C, holding time need not be longer than 2 to 3 h to fulfil the implicit requirements of the German Standard (DIN 18516). On the other hand, literature data show that it should be possible to further shorten this holding time if it were possible to heat up faster and more homogeneously the glass to be tested

Un cadre général pour l'analyse des conflits

National audienceCet article présente plusieurs contributions au "Conflict Driven Clauses Learning" (CDCL), qui est une des composantes clés des solveurs SAT mo- dernes. Tout d'abord, nous montrons que, à partir du graphe d'implication, les clauses assertives obtenues en utilisant le principe du premier point d'implication unique ("First Unique Implication Point" (FUIP)) sont optimales en terme de saut arrière. Puis nous propo- sons une extension du graphe d'implication contenant de nouveaux arcs appelés arcs arrières. Ces arcs sont obtenus en tenant compte des clauses satisfaites qui sont habituellement ignorées par l'analyse du conflit. Cette extension capture plus fidèlement l'ensemble du processus de propagation et ouvre de nouvelles pers- pectives pour les approches fondées sur CDCL. Entre autres avantages, notre extension du graphe d'impli- cation conduit à un nouveau schéma d'analyse des conflits qui exploite les arcs ajoutés et permet des retours arrières plus haut dans l'arbre de recherche. Les résultats expérimentaux montrent que l'intégration de notre système d'analyse des conflits généralisés au sein de solveurs dernier-cri améliore sensiblement leurs performances

Un cadre général pour l'analyse de conflits

National audienceCet article présente plusieurs contributions au "Conflict Driven Clauses Learning" (CDCL), qui est une des composantes clés des solveurs SAT modernes. Tout d'abord, nous montrons que, à partir du graphe d'implication, les clauses assertives obtenues en utilisant le principe du premier point d'implication unique ("First Unique Implication Point" (FUIP)) sont optimales en terme de saut arrière. Puis nous proposons une extension du graphe d'implication contenant de nouveaux arcs appelés arcs arrières. Ces arcs sont obtenus en tenant compte des clauses satisfaites qui sont habituellement ignorées par l'analyse du conflit. Cette extension capture plus fidèlement l'ensemble du processus de propagation et ouvre de nouvelles perspectives pour les approches fondées sur CDCL. Entre autres avantages, notre extension du graphe d'implication conduit à un nouveau schéma d'analyse des conflits qui exploite les arcs ajoutés et permet des retours arrières plus haut dans l'arbre de recherche. Les résultats expérimentaux montrent que l'intégration de notre système d'analyse des conflits généralisés au sein de solveurs dernier-cri améliore sensiblement leurs performances

On the stochastic constraint satisfaction framework

Stochastic constraint satisfaction is a framework that allows to make decisions taking into account possible futures. We study two challenging aspects of this framework: (1) variables in stochastic CSP are ordered sequentially, which is adequate for the representation of a number of problems, but is not a natural choice for the modeling of problems in which the future can follow different branches (2) the framework was designed to allow multi-objective decision-making, yet this issue has been treated only superficially in the literature. We bring a number of clarifications to these two aspects. In particular, we show how minor modifications allow the framework to deal with non-sequential forms, we identify a number of technicalities related to the use of the sequential ordering of variables and of the use of multiple objectives, and in addition we propose the first search algorithm that solves multi-objective stochastic problems in polynomial space

A solver for quantified Boolean and linear constraints

We make a number of contributions to the understanding and practical resolution of quantified constraints. Unlike previous work in the CP literature that was essentially focused on constraints expressed as binary tables, we focus on Presburger Arithmetics, i.e., Boolean combinations of linear constraints. From a theoretical perspective, we clarify the problem of the treatment of universal quantifiers by proposing a “symmetric ” version of the notion of quantified consistency. This notion imposes to maintain two constraint stores, which will be used to reason on universal and existential variables, respectively. We then describe a branch & bound algorithm that integrates both forms of propagation. Its implementation is, to the best of our knowledge, the first CP solver for this class of quantified constraints. 1

CSP properties for quantified constraints: Definitions and complexity

Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the simple, classical notion of solution inappropriate. As a consequence, even such essential CSP properties as consistency or substitutability are not completely understood in the quantified case. In this paper, we show that most of the properties which are used by solvers for CSP can be generalized to Quantified CSP. We propose a systematic study of the relations which hold between these properties, as well as complexity results regarding the decision of these properties. Finally, and since these problems are typically intractable, we generalise the approach used in CSP and propose weakenings of these notions based on locality, which allow for a tractable, albeit incomplete detecting of these properties

A solver for quantified Boolean and linear constraints

Abstract. We make a number of contributions to the understanding and practical resolution of quantified constraints. Unlike previous work in the CP literature that was essentially focused on constraints expressed as binary tables, we focus on Presburger Arithmetics, i.e., Boolean combinations of linear constraints. We explain why we think this language is especially interesting. From a theoretical perspective, we clarify the problem of the treatment of universal quantifiers by proposing a “symmetric” version of the notion of quantified consistency. This notion imposes to maintain two constraint stores, which will be used to reason on universal and existential variables, respectively. We then describe an implementation of a branch & bound algorithm that integrates both forms of propagation and that is, to the best of our knowledge, the first implementation of a CP solver for this class of quantified constraints.