Applying interval arithmetic to real, integer, and boolean constraints

Benhamou, Frédéric; Older, William J.

doi:10.1016/s0743-1066(96)00142-2

Cited by 212 publications

(148 citation statements)

References 8 publications

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“…In Cleary's work constraint systems are processed by hull-consistency, a consistency property exploiting the convex hull of (in)equalities over the reals. These pioneering ideas have been extended in several ways, e.g., for heterogeneous constraint processing [6] or implementing strong consistencies [46]. CLP(BNR) [56] was the premier CLP system using interval consistency techniques.…”

Section: Interval Consistency Techniquesmentioning

confidence: 99%

“…But the user still gets the feel of interval arithmetic: The implementation with range arithmetic is still essentially interval based, and these intervals may grow too large during computations leading to failures due to insufficient precision. An implementation of the sequence for the logistic equation (2) may look as follows: long n, prec; cin >> n; cin >> prec; set_precision(prec); real x=1/real(2); real c=375/real(100); for (i=1; i <= n; i++) { x=c*x*(one-x); if (i%10==0) cout<<i<<" "<<x.str (2,20)<<endl; } If the second input parameter prec is too small for a first parameter 6 . the program fails.…”

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confidence: 99%

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Novel Approaches to Numerical Software with Result Verification

Granvilliers

Kreinovich

Müller

2004

Numerical Software With Result Verification

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Section: Interval Consistency Techniquesmentioning

confidence: 99%

mentioning

confidence: 99%

Novel Approaches to Numerical Software with Result Verification

Granvilliers

Kreinovich

Müller

2004

Numerical Software With Result Verification

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“…Interval constraint propagation (ICP) makes it possible (Benhamou and Older, 1997) to generate a sequence of nested axis-aligned subboxes [q] of [p] which enclose the posterior feasible set 5 de ned by (1). As these methods are not branch-and-bounds based, they can easily deal with high-dimensional problems.…”

Section: Interval Constraint Propagationmentioning

confidence: 99%

“…A constraint is a subset P of R n (see, Benhamou and Older, 1997): Here, we shall consider only constraints of the form…”

Section: Reduction With One Constraintmentioning

confidence: 99%

Interval constraint propagation with application to bounded-error estimation

Jaulin¹

2000

Automatica

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For a large class of bounded-error estimation problems, the posterior feasible set 5 for the parameters can be de ned by nonlinear inequalities. The set-inversion approach combines classical interval analysis with branch-and-bound algorithms to characterize 5. Unfortunately, as bisections have to be done in all directions of the parameter space, this approach is limited to problems involving a small number of parameters. Techniques based on interval constraint propagation make it possible to drastically reduce the number of bisections. In this paper, these techniques are combined with set inversion to bracket 5 between inner and outer subpavings (union of nonoverlapping boxes). When only interested in the feasible intervals for the parameters, the set inversion approach becomes ine¢cient, and a new algorithm able to compute these intervals is given. This algorithm uses a new interval-based local research to compute the smallest box that contains 5. It is then compared with existing methods on an example taken from the literature.

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“…Constraints are arithmetic constraints over integers and equality/disequality constraints over terms. We will use D to denote the underlying domain structure which interprets arithmetic constraints over integers and equality/disequality constraints over terms in the usual way [6,8]. There is no complete constraint solver for arbitrary integer arithmetic constraints.…”

Section: Syntaxmentioning

confidence: 99%