Finite domain constraint programming systems

Tutorial at CP'2002, Principles and Practice of Constraint Programming. Powerpoint slides.</p

An Improved Tight Closure Algorithm for Integer Octagonal Constraints

Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality'' or ``UTVPI integer constraints'') constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint programming and formal analysis and verification of software and hardware systems, since they couple algorithms having polynomial complexity with a relatively good expressive power. The main algorithms required for the manipulation of such constraints are the satisfiability check and the computation of the inferential closure of a set of constraints. The latter is called `tight' closure to mark the difference with the (incomplete) closure algorithm that does not exploit the integrality of the variables. In this paper we present and fully justify an O(n^3) algorithm to compute the tight closure of a set of UTVPI integer constraints.Comment: 15 pages, 2 figure

Adaptation d'un algorithme optimal d'ordonnancement en régime permanent pour des lots bornés

International audienceLe contexte de cet article est l ordonnancement de lots bornes de travaux identiques sur une plate-forme d execution heterogene comme la grille. Les travaux executes sont des graphes de t?ches orientes et sans cycle (DAG), en forme d anti-arbre. Les t?ches sont de plusieurs types et les n{oe}uds de la plate-forme ne sont pas toujours en mesure d executer tous les types de t?ches. Le probleme de minimisation du temps d execution d un lot est un probleme NP-Complet. Sous l angle du regime permanent, il est possible de decrire le probleme sous la forme d un programme lineaire donnant une solution optimale pour l ordonnancement cyclique de lots infinis. Lorsque les lots sont bornes, les resultats restent bons bien que sous optimaux. Nous montrons ici que les phases d initialisation et de terminaison ajoutent un sur-co?t qui penalise le temps global d execution. Nous montrons ensuite le lien entre la taille de ces phases et la taille de la periode de l ordonnancement cyclique et donnons un algorithme permettant le calcul de la periode minimale. Des experimentations, obtenues par simulations avec SimGrid, illustrent en fin d article le gain apporte par le choix d une periode minimal

Efficient Generation of Craig Interpolants in Satisfiability Modulo Theories

The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for effective decision procedures, called Satisfiability Modulo Theory solvers. We make the following contributions. First, we provide interpolation procedures for several basic theories of interest: the theories of linear arithmetic over the rationals, difference logic over rationals and integers, and UTVPI over rationals and integers. Second, we define a novel approach to interpolate combinations of theories, that applies to the Delayed Theory Combination approach. Efficiency is ensured by the fact that the proposed interpolation algorithms extend state of the art algorithms for Satisfiability Modulo Theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more efficiently than other competitor solvers.Comment: submitted to ACM Transactions on Computational Logic (TOCL

Optimal certifying algorithms for linear and lattice point feasibility in a system of UTVPI constraints

This thesis is concerned with the design and analysis of time-optimal and spaceoptimal, certifying algorithms for checking the linear and lattice point feasibility of a class of constraints called Unit Two Variable Per Inequality (UTVPI) constraints. In a UTVPI constraint, there are at most two non-zero variables per constraint, and the coefficients of the non-zero variables belong to the set {lcub}+1, --1{rcub}. These constraints occur in a number of application domains, including but not limited to program verification, abstract interpretation, and operations research. As per the literature, the fastest known certifying algorithm for checking lattice point feasibility in UTVPI constraint systems ([1]), runs in O( m n + n2 log n) time and O(n2) space, where m represents the number of constraints and n represents the number of variables in the constraint system. In this paper, we design and analyze new algorithms for checking the linear feasibility and the lattice point feasibility of UTVPI constraints. Both of the presented algorithms run in O( m[.]n) time and O(m + n) space. Additionally they are certifying in that they produce satisfying assignments in the event that they are presented with feasible instances and refutations in the event that they are presented with infeasible instances. The importance of providing certificates cannot be overemphasized, especially in mission-critical applications. Our approaches for both the linear and the lattice point feasibility problems in UTVPI constraints are fundamentally different from existing approaches for these problems (as described in the literature), in that our approaches are based on new insights on using well-known inference rules

XCSP3-core: A Format for Representing Constraint Satisfaction/Optimization Problems

In this document, we introduce XCSP3-core, a subset of XCSP3 that allows us to represent constraint satisfaction/optimization problems. The interest of XCSP3-core is multiple: (i) focusing on the most popular frameworks (CSP and COP) and constraints, (ii) facilitating the parsing process by means of dedicated XCSP3-core parsers written in Java and C++ (using callback functions), (iii) and defining a core format for comparisons (competitions) of constraint solvers.Comment: arXiv admin note: substantial text overlap with arXiv:1611.0339