By Marie Pelleau
Constraint Programming goals at fixing not easy combinatorial difficulties, with a computation time expanding in perform exponentially. The tools are this present day effective adequate to resolve huge business difficulties, in a typical framework. besides the fact that, solvers are devoted to a unmarried variable sort: integer or actual. fixing combined difficulties is determined by advert hoc ameliorations. In one other box, summary Interpretation deals instruments to end up application homes, through learning an abstraction in their concrete semantics, that's, the set of attainable values of the variables in the course of an execution. a number of representations for those abstractions were proposed. they're referred to as summary domain names. summary domain names can combine any kind of variables, or even symbolize kinfolk among the variables.
In this paintings, we outline summary domain names for Constraint Programming, with a view to construct a known fixing technique, facing either integer and actual variables. We additionally examine the octagons summary area, already outlined in summary Interpretation. Guiding the hunt by way of the octagonal relatives, we receive stable effects on a continuing benchmark. We additionally outline our fixing process utilizing summary Interpretation thoughts, as a way to contain latest summary domain names. Our solver, AbSolute, is ready to clear up combined difficulties and use relational domains.
- Exploits the over-approximation the right way to combine AI instruments within the equipment of CP
- Exploits the relationships captured to unravel non-stop difficulties extra effectively
- Learn from the builders of a solver in a position to dealing with essentially all summary domains
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Extra resources for Abstract Domains in Constraint Programming
Note that in both the discrete and continuous cases, the resolution process can be modiﬁed in order to stop as soon as the ﬁrst solution is found. In both solving methods, the selection criterion of the variable to instantiate or domain to cut is not explicitly given. This is because there is no unique way to choose the domain to be cut or the variable to instantiate, and it often depends on the problem to solve. The next State of the Art 43 section describes some of the choice strategies or existing exploration strategies.
Let C : v1 + v2 ≤ 3 be a constraint. e. C(2, 0) is true. In contrast, C(2, 2) is false. In the case of real domains, an important feature is that constraints can answer: – true, if the box only contains solutions; – false, if the box contains no solution at all; – maybe, when we cannot determine whether the box contains solutions or not. This can happen when a box contains both solution and non-solution elements. 30 Abstract Domains in Constraint Programming These different answers are due to the interval arithmetic [MOO 66].
Note that there may be no abstraction function and no narrowing operator, and, although relatively rare, there can be no join. 5, the polyhedra abstract domain has no abstraction function, and therefore no Galois connection. Moreover, it does not feature any narrowing operator. Although they may not exist, these different operators are useful in order to have only one possible representation for a given concrete domain (abstraction) and to reﬁne the overapproximation while computing the ﬁxpoint (narrowing).
Abstract Domains in Constraint Programming by Marie Pelleau