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Constraint Arithmetic on Real Intervals
, 1993
"... Constraint interval arithmetic is a sublanguage of BNR Prolog which offers a new approach to the old problem of deriving numerical consequences from algebraic models. Since it is simultaneously a numerical computation technique and a proof technique, it bypasses the traditional dichotomy between (nu ..."
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Cited by 67 (3 self)
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Constraint interval arithmetic is a sublanguage of BNR Prolog which offers a new approach to the old problem of deriving numerical consequences from algebraic models. Since it is simultaneously a numerical computation technique and a proof technique, it bypasses the traditional dichotomy between (numeric) calculation and (symbolic) proofs. This interplay between proof and calculation can be used effectively to handle practical problems which neither can handle alone. The underlying semantic model is based on the properties of monotone contraction operators on a lattice, an algebraic setting in which fixed point semantics take an especially elegant form.
Arbitrary Precision Real Arithmetic: Design and Algorithms
, 1996
"... this article the second representation mentioned above. We first recall the main properties of computable real numbers. We deduce from one definition, among the three definitions of this notion, a representation of these numbers as sequence of finite Badic numbers and then we describe algorithms fo ..."
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Cited by 19 (0 self)
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this article the second representation mentioned above. We first recall the main properties of computable real numbers. We deduce from one definition, among the three definitions of this notion, a representation of these numbers as sequence of finite Badic numbers and then we describe algorithms for rational operations and transcendental functions for this representation. Finally we describe briefly the prototype written in Caml. 2. Computable real numbers
Optimal Interval Enclosures For FractionallyLinear Functions, And Their Aplication To Intelligent Control
, 1992
"... One of the main problems of interval computations is, given a function f(x 1 ; :::; x n ) and n intervals x 1 ; :::; x n , to compute the range y = f(x 1 ; :::; x n ). This problem is feasible for linear functions f , but for generic polynomials, it is known to be computationally intractable. Becaus ..."
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Cited by 13 (5 self)
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One of the main problems of interval computations is, given a function f(x 1 ; :::; x n ) and n intervals x 1 ; :::; x n , to compute the range y = f(x 1 ; :::; x n ). This problem is feasible for linear functions f , but for generic polynomials, it is known to be computationally intractable. Because of that, traditional interval techniques usually compute the enclosure of y, i.e., an interval that contains y. The closer this enclosure to y, the better. It is desirable to describe cases in which we can compute the optimal enclosure, i.e., the range itself.
Computing Time Intervals Logically
"... The purpose of using firstorder logic to program a computer is to turn the task of programming into the task of expressing relations that must be jointly satisfiable. One obstacle to relational and logical programming has been arithmetic, which is usually evaluated functionally. This paper ..."
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The purpose of using firstorder logic to program a computer is to turn the task of programming into the task of expressing relations that must be jointly satisfiable. One obstacle to relational and logical programming has been arithmetic, which is usually evaluated functionally. This paper