We extend the conventional BDD-based model checking algorithms to verify systems with non-linear arithmetic constraints. We represent each constraint as a BDD variable, using the information from a constraint solver to prune the BDDs by removing paths that correspond to infeasible constraints. We illustrate our technique with a simple example, which has been analyzed with our prototype implementation. 1

. An appropriate combination of symbolic and numeric solvers often makes it possible to solve problems that none of these solvers can tackle alone. In this paper, we specify a cooperative architecture which allows using concurrently heterogeneous solvers when handling constraints over the reals. This architecture is based upon agents that communicate via asynchronous message passing. Agents are synchronized when a failure or a success occurs. Disjunctive constraints are handled by backtracking. Operational semantics and terminating conditions of such systems are discussed. Implementation issues are addressed. We end the presentation by several examples and give some computational results from a first prototype. 1 Introduction 1.1 Motivation Many industrial applications can be modeled by a set of constraints defined over the reals (e.g., financial applications, thermal flow problems, electro-mechanical engineering problems) . These systems of constraints are usually non-linear or even...

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 CoSAc (Constraint System Architecture) 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.

. In this paper we introduce a cooperative scheme for solving systems of constraints over the reals. First, we informally show how an appropriate combination of symbolic and numeric solvers makes it possible to solve problems that none of these solvers can tackle alone. Then, we specify a cooperative architecture which allows to use concurrently heterogeneous solvers when handling constraints over the reals. This architecture is based upon agents that communicate via asynchronous message passing. Agent are synchronized when a failure or a success occurs. Disjunctive constraints are handled by backtracking. Operational semantics and terminating conditions of such systems are discussed. Message processing is detailed for both the general case where several non-deterministic solvers are involved in the cooperation, and for more specialized architectures. 1 Introduction 1.1 Motivation Numerous industrial problems can be modeled by a set of constraints defined over the reals (e.g., financ...

Numerical constraint systems are often handled by branch and prune algorithms that combine splitting techniques, local consistencies, and interval methods. This paper first recalls the principles of Quad, a global constraint that works on a tight and safe linear relaxation of quadratic subsystems of constraints. Then, it introduces a generalization of Quad to polynomial constraint systems. It also introduces a method to get safe linear relaxations and shows how to compute safe bounds of the variables of the linear constraint system. Different linearization techniques are investigated to limit the number of generated constraints. QuadSolver, a new branch and prune algorithm that combines Quad, local consistencies, and interval methods, is introduced. QuadSolver has been evaluated on a variety of benchmarks from kinematics, mechanics, and robotics. On these benchmarks, it outperforms classical interval methods as well as constraint satisfaction problem solvers and it compares well with state-of-the-art optimization solvers.

this paper we go a step further and propose an extension mechanism which allows for the `on-the-y' generation of lemmas. This is an important improvement since|if suitably coupled with a lemma speculation facility|it relieves the user from the burden of providing lemmas in many situations thereby resulting in increased automation. Furthermore, in order to show its practical usability, we illustrate how our schema can lift a decision procedure for the quantier-free fragment of Presburger Arithmetic to tackle non-linear problems of signicant diculty, based on anization techniques [6].

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The goals of this thesis were to investigate the applicability of genetic algorithms to the problem of real-time scheduling of aircraft landings. In particular we investigate whether the constraints and the constantly changing conditions can be represented and whether adequate schedules can be computed in the time available. When a new plane needs to be placed in the schedule, the best schedules from the previous iteration are used as the starting point. We tested the genetic algorithm in generating landing schedules for ten data sets of aircraft landing data of between 30 and 40 planes. The genetic approach is compared with the performance of a heuristic search and currently it does not perform as well. The results indicate that good solutions can be obtained in a reasonable time, however it is apparent that the parameters for the genetic algorithm could be fine tuned, to produce better results. Contents 1 Introduction 4 1.1 Goals : : : : : : : : : : : : : : : : : : : : : : : : : ...

This paper presents a quadratic optimiser for solving quadratic programming optimisation problem in constraint logic programming paradigm. Quadratic programming optimisation problems are a subclass of the general nonlinear programming optimisation problems in operational research. The optimiser showed fast convergence over the tested problems. It enriched the CLP(R) in Sicstus Prolog with the capability of quadratic programming optimisation in addition to the existing capability of linear programming optimisation which opens further domain of applications to CLP. Moreover, it could be extended to be used by successive quadratic programming method to solve a large class of nonlinear optimisation problems. Introduction Logic programming (LP) languages are a form of declarative languages based on Horn Clause logic. This family of languages has been known for sometime but it became more practical and more reliable after introducing the Warren abstract machine [31] in 1983. The idea of LP ...

Retrofit of heat exchanger networks (RHEN) has not taken as much attention in the literature as the grass-roots design of heat exchanger networks (HEN). The problem has been partially solved, either with optimisation techniques which failed in real life large scale applications or with pinch technology which did not offer much help for RHEN in contrast with grass-roots design of HEN. In this thesis, two new methods for solving RHEN problems are introduced. In both methods, we have utilised constraint logic programming (CLP) as a powerful paradigm to solve the problem. In the first method, retrofit by inspection, CLP was used as a mechanism to prune the search space. We have updated and formalised the guidelines introduced by Lakshmanan[34] in 1996. The second method is Smart-RHEN, a new approach that we have developed to solve RHEN problem. SMART-RHEN is a three stage algorithm that starts by growing a large network, fitting the current network, and lastly pruning the network to achiev...