F. Benhamou and W. Older, "Applying Interval Arithmetic to Real Integer and Boolean Constraints", Journal of Logic Programming 32(3ng 1997  Home/Search   Document Details and Download   Summary   Related Articles   Check

....method only removes inconsistent values and may not remove all such values, it may be that the resulting intervals contain no solution. Thus, results in the consistency method have the meaning: if a solution exists, then it is in the intervals found. Some references to interval constraints are [4, 5, 15, 16]. 3.3. Interval Constraint Plotting Conventional plotting, because of the single for loop, is linear, but restricted to functions. Raster scan plotting handles relations, but is quadratic. It might be thought that quadraticity is inherent in the ability to handle relations. This is not so. ....

Benhamou, F. and W. Older, "Applying Interval Arithmetic to Real, Integer, and Boolean Constraints," Journal of Logic Programming, 32(1), 1997, pp. 1--24.

....logic semantics is preserved, i.e. answers are logical consequences of declarative logic programs, even when floating point computations have been used. These reasons have motivated the development of numerous CLP systems based on interval arithmetic (e.g. BNR Prolog [20] Newton [1] CLP(BNR) [3], Interlog [12, 5, 14] Prolog IV [4] All these systems use an arc consistency like algorithm [17] adapted for numeric constraints [8, 7] The standard interval narrowing algorithm has two main limitations : ffl the so called problem of early quiescence [8] i.e. the algorithm stops before ....

F. Benhamou and W. Older, `Applying interval arithmetic to real, integer and boolean constraints', Journal of Logic Programming, (1994).

....engineering problems involve solving arbitrary constraints over the reals. Such systems of constraints are usually mixed: they are formed of linear equalities and inequalities, non linear equalities and often non polynomial ones. Interval arithmetic has been introduced in the CLP framework [9, 15, 13, 2, 1, 21] because of its capabilities to narrow the domains of the variables for any system of constraints over the reals. We collectively call the local consistency algorithms used in these systems IN algorithms 1 . Chiu and Lee [5, 6] show that existing CLP languages based upon IN algorithms are ....

....are actually incorporated within the constraint store of the other solver while its solving processes are still working. reliablecomputing97.tex; 3 06 1997; 11:33; no v. p.4 Concurrent Cooperating Solvers Over The Reals 5 2.1. The IN Solver CLP systems like BNR Prolog [15] Newton [1] CLP(BNR) [2], Interlog [13] and Prolog IV [8] use a narrowing algorithm adapted from the Waltz algorithm [23] which computes an approximation of arc consistency [9] The general scheme of this fixed point algorithm is given in figure 1. C = fC 1 ; Cm g denotes a set of constraints over X = fx 1 ....

F. Benhamou and W. Older, `Applying interval arithmetic to real, integer and boolean constraints', Journal of Logic Programming, (1994).

....since the paradigm is parallel by nature. The runtime behavior of the algorithm is influenced by its parameters. The fitness function itself plays a crucial role in the calculation and does not only 1 The case of inequations can be reduced to this case and the application of interval arithmetic [11, 12]. Fitness function Current Generation Next Generation Repeat Sort solutions based on fitness function Select best solutions to keep Crossover Mutation and other operations Figure 4: Architecture of a Genetic Algorithm. influence the quality of the results, but also the overall performance of ....

F. Benhamou J.Older. Applying interval arithmetic to real integer and boolean constraints. Logic Programming: The Alp Newsletter, 6(2), 1993.

....solutions must involve a mechanism such as backtracking or or parallelism. This technique, since it works by removing non solutions, can be regarded as a model elimination proof procedure, and this gives it quite different charateristics from constructivist exact arithmetic systems. As shown in [Benhamou and Older 1992], a major advantage of this approach is that it provides a uniform treatment of a wide range of problems usually treated by very different methods. CLP(BNR) currently deals with boolean variables, the natural numbers, and the reals, and supports a large number of primitive relations. Because they ....

.... effectively to solve scheduling problems with mutually exclusive resource allocation such as the bridge problem described in [Van Hentenryck 1989] The CLP(BNR) program for this problem, which involves forty six tasks and more than six hundred constraints, is described in detail in the appendix to [Benhamou and Older 1992]. 4 Magic Series Mixed boolean and integer constraints can be used to solve puzzles like the magic series [Colmerauer 1990, Van Hentenryck 1989] The problem here is to find a sequence of non negative integers (x 0 ; x n Gamma1 ) such that, for every i in f0; n Gamma 1g, x i is the ....

Benhamou F. and Older W. "Applying Interval Arithmetic to Real, Integer and Boolean Constraints" BNR Research Report, 1992.

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F. Benhamou and W. Older, "Applying Interval Arithmetic to Real Integer and Boolean Constraints", Journal of Logic Programming 32(3ng 1997

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F. Benhamou and W. Older. Applying interval arithmetic to real integer and boolean constraints. Journal of Logic Programming, 32(1):1-- 24, 1997.

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