We consider constraint satisfaction problemswith variables in continuous,numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.

Logic programming realizes the ideal of "computation is deduction," but not when floating-point numbers are involved. In that respect logic programming languages are as careless as conventional computation: they ignore the fact that floating-point operations are only approximate and that it is not easy to tell how good the approximation is. It is our aim to extend the benefits of logic programming to computation involving floating-point arithmetic. Our starting points are the ideas of Cleary and the CHIP programming language. Cleary proposed a relational form of interval arithmetic which was incorporated in BNR Prolog in such a way that variables already bound can be bound again. In this way the usual logical interpretation of computation no longer holds. In this paper we develop a technique for narrowing intervals that we relate both to Cleary's work and to the constraint-satisfaction techniques of artificial intelligence. We then modify CHIP by allowing domains to be intervals of rea...

Existing interval constraint logic programming languages, such as BNR Prolog, work under the framework of interval narrowing and are deficient in solving linear systems, which constitute an important class of problems in engineering and other applications. In this paper, an interval linear equality solver, which is based on generalized interval arithmetic and Gaussian elimination, is proposed. We show how the solver can be adapted to incremental execution and incorporated into a constraint logic programming language already equipped with a non-linear solver based on interval narrowing. The two solvers interact and cooperate during computation, resulting in a practical interval constraint arithmetic language CIAL. A prototype of CIAL, based on CLP(R), is constructed and compared favourably against several major constraint logic programming languages.

We propose the use of the preconditioned interval Gauss-Seidel method as the backbone of an efficient linear equality solver in a CLP(Interval) language. The method, as originally designed, works only on linear systems with square coefficient matrices. Even imposing such a restriction, a naive incorporation of the traditional preconditioning algorithm in a CLP language incurs a high worst-case time complexity of O(n^4), where n is the number of variables in the linear system. In this paper, we generalize the algorithm for general linear systems with m constraints and n variables, and give a novel incremental adaptation of preconditioning of O(n 2 (n + m)) complexity. The efficiency of the incremental preconditioned interval Gauss-Seidel method is demonstrated using large-scale linear systems.

As a logic programming language, Prolog has shortcomings. One of the most serious of these is in arithmetic. CLP(R), though a vast improvement, assumes perfect arithmetic on reals, an unrealistic requirement for computers, where there is strong pressure to use floatingpoint arithmetic. We present an adaptation of CLP(R) where the errors due to floating-point computation are absorbed by the use of intervals in such a way that the logical status of answers is not jeopardized. This system is based on Cleary's "squeezing" of floating-point intervals, modified to fit into Mackworth's general framework of the Constraint-Satisfaction Problem. Our partial implementation consists of a meta-interpreter executed by an existing CLP(R) system. All that stands in the way of correct answers involving real numbers is the planned addition of outward rounding to the current prototype. 1 Introduction Mainstream computing holds that programming should be improved by gradual steps, as exemplified by the m...

We present a generic framework for defining and solving interval constraints on any set of domains (finite or infinite) that are lattices. The approach is based on the use of a single form of constraint similar to that of an indexical used by CLP for finite domains and on a particular generic definition of an interval domain built from an arbitrary lattice. We provide the theoretical foundations for this framework and a schematic procedure for the operational semantics. Examples are provided that illustrate how new (compound) constraint solvers can be constructed from existing solvers using lattice combinators and how different solvers (possibly on distinct domains) can communicate and hence, cooperate in solving a problem. We describe the language clp(L), which is a prototype implementation of this framework and discuss ways in which this implementation may be improved.

This paper reviews work on using interval arithmetic as the basis for next generation spreadsheet programs capable of dealing with rounding errors, imprecise data, and numerical constraints. A series of ever more versatile computational models for spreadsheets are presented beginning from classical interval arithmetic and ending up with interval constraint satisfaction. In order to demonstrate the ideas, an actual implementation of each model as a class library is presented and its integration with a commercial spreadsheet program is explained. 1 LIMITATIONS OF SPREADSHEET COMPUTING Spreadsheet programs, such as MS Excel, Quattro Pro, Lotus 1--2--3, etc., are among the most widely used applications of computer science. Since the pioneering days of VisiCalc and others, spreadsheet programs have been enhanced immensely with new features. However, the underlying computational paradigm of evaluating arithmetical functions by using ordinary machine arithmetic has remained the same. The wor...

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The process of understanding a source code in a high-level programming language is a complex cognitive task. The provision of helpful decision aid subsystems would be of great benefit to software maintainers. Given a library of program plan templates, generating a partial understanding of a piece of software source code can be shown to correspond to the construction of mappings between segments of the source code and particular program plans represented in a library of domain source programs (plans). These mappings can be used as part of the larger task of reverse engineering source code, to facilitate many software engineering tasks such as software reuse, and for program maintenance. We present a novel model of program understanding using constraint satisfaction. The model composes a partial global picture of source program code by transforming knowledge about the problem domain and the program structure into constraints. These constraints facilitate the efficient construction of ma...

It is well known that the expressive power and efficiency of Constraint Logic Programming (CLP) systems is reduced by the strong partitioning of the domains in which constraints can be expressed. This means constraints defined on a particular domain must be solved by a specific reasoning method with its associated solver that is not appropriate for constraints defined on other domains. In this paper, we describe a common unified framework for constraints on any computation domain in which an ordering has been defined. It is based on a single generic constraint and unique inference rule. We demonstrate, through examples, the expressiveness of our framework on a number of domains.