Abstract Domains in Constraint Programming by Marie Pelleau

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 commercial difficulties, in a conventional framework. despite the fact that, solvers are devoted to a unmarried variable variety: integer or actual. fixing combined difficulties depends on advert hoc variations. In one other box, summary Interpretation deals instruments to turn out 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 known as summary domain names. summary domain names can combine any kind of variables, or even characterize relatives among the variables.

In this paintings, we outline summary domain names for Constraint Programming, which will construct a customary fixing procedure, facing either integer and actual variables. We additionally research the octagons summary area, already outlined in summary Interpretation. Guiding the quest by way of the octagonal family members, we receive reliable effects on a continuing benchmark. We additionally outline our fixing process utilizing summary Interpretation strategies, as a way to comprise present summary domain names. Our solver, AbSolute, is ready to resolve combined difficulties and use relational domains.

  • Exploits the over-approximation tips on how 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 in a position to dealing with virtually all summary domains

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Extra resources for Abstract Domains in Constraint Programming

Sample text

Lower closure operators may be reformulated as a fixpoint. This unifies the use of narrowings and brings out the similarities in the iterative computations. Given an element X, ρ computes the greatest fixpoint smaller than X, that is ρ(X) = gfpX ρ. Local iterations may be used at any time in the analysis and not only after a widening. Given a program to analyze, an abstract domain is chosen to best represent the program properties. There exist several types of abstract domains. A brief presentation of abstract domains is given in the next section.

The propagation loop applies the HC4-Revise algorithm seen earlier for each constraint containing at least one variable that has been modified. More recently, the Mohc algorithm studying the monotony of the constraints to propagate has been developed [ARA 10, ARA 12]. 3. Exploration Generally, the propagation is not sufficient to find the solutions. During the second step of the resolution process, assumptions about the variables values are made. In the case of integer variables, values are given to variables iteratively until a success (a solution is found) or a fail (a constraint is false, an empty domain) is obtained.

Therefore, every operator in D must have an abstraction in D . These different operators are listed below. Operators on abstract domains: – a concretization function γ : D → D , and if it exists an abstraction function α : D → D forming a Galois connection D γ ← −→ −D ; −− α – a least element ⊥ and a greatest element and γ( ) = V with D = P(V ); such that γ(⊥ ) = ∅ – efficient algorithms to compute transfer functions; 24 Abstract Domains in Constraint Programming – efficient algorithms for the meet ∪ and join ∩ ; – efficient algorithms for the widening increasing chain; if D has an infinite – if it exists and D has an infinite decreasing chain, efficient algorithms for the narrowing .

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