Abstract Domains in Constraint Programming by Marie Pelleau

By Marie Pelleau

Constraint Programming goals at fixing demanding combinatorial difficulties, with a computation time expanding in perform exponentially. The tools are this day effective adequate to resolve huge commercial difficulties, in a wide-spread framework. notwithstanding, solvers are devoted to a unmarried variable sort: integer or actual. fixing combined difficulties is dependent upon advert hoc changes. In one other box, summary Interpretation deals instruments to turn out software houses, by way of learning an abstraction in their concrete semantics, that's, the set of attainable values of the variables in the course of an execution. numerous representations for those abstractions were proposed. they're referred to as summary domain names. summary domain names can combine any form of variables, or even characterize kinfolk among the variables.

In this paintings, we outline summary domain names for Constraint Programming, with the intention to construct a typical fixing procedure, facing either integer and genuine variables. We additionally research the octagons summary area, already outlined in summary Interpretation. Guiding the hunt by means of the octagonal family, we receive reliable effects on a continuing benchmark. We additionally outline our fixing process utilizing summary Interpretation concepts, so one can comprise present summary domain names. Our solver, AbSolute, is ready to clear up combined difficulties and use relational domains.

  • Exploits the over-approximation ways to combine AI instruments within the tools of CP
  • Exploits the relationships captured to resolve non-stop difficulties extra effectively
  • Learn from the builders of a solver able to dealing with essentially all summary domains

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Recent years have seen the development of many new abstract domains capturing other properties, such as octagons [MIN 06], ellipsoids [FER 04], octahedra [CLA 04] and even varieties [ROD 04]. In addition, support libraries for abstract domains, such as Apron [JEA 09], were designed. These new domains can handle all kinds of numeric variables, mathematical integers, rationals, reals, machine integers and floating-point numbers [MIN 12]. They even express relationships between variables of different types [MIN 04], and between numeric and Boolean variables [BER 10].

There exist several types of abstract domains. A brief presentation of abstract domains is given in the next section. 6. Abstract domains Abstract domains play a key role in AI. Because of the importance of numerical properties and variables in a program, many numerical abstract domains are developed. Major numerical abstract domains include intervals [COU 77a] and polyhedra [COU 78]. Recent years have seen the development of many new abstract domains capturing other properties, such as octagons [MIN 06], ellipsoids [FER 04], octahedra [CLA 04] and even varieties [ROD 04].

Constraint satisfaction For integer variables, given an instantiation for the variables, a constraint answers true if this variables assignment satisfies the constraint, and false otherwise. – Let v1 and v2 be two integer variables with domains D1 = 0, 2 and D2 = 0, 2 . 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.

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