Download Abstract Domains in Constraint Programming by Marie Pelleau PDF

By Marie Pelleau

ISBN-10: 1785480103

ISBN-13: 9781785480102

Constraint Programming goals at fixing difficult combinatorial difficulties, with a computation time expanding in perform exponentially. The tools are this present day effective sufficient to unravel huge commercial difficulties, in a typical framework. despite the fact that, solvers are devoted to a unmarried variable style: integer or actual. fixing combined difficulties depends on advert hoc modifications. In one other box, summary Interpretation deals instruments to end up application homes, by means 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 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, with a view to construct a conventional fixing procedure, facing either integer and actual variables. We additionally learn the octagons summary area, already outlined in summary Interpretation. Guiding the hunt by means of the octagonal family members, we receive solid effects on a continuing benchmark. We additionally outline our fixing process utilizing summary Interpretation suggestions, with a purpose to contain current summary domain names. Our solver, AbSolute, is ready to remedy combined difficulties and use relational domains.

  • Exploits the over-approximation how you can combine AI instruments within the tools 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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Additional info for Abstract Domains in Constraint Programming

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Y ); State of the Art 21 Granger’s work [GRA 92] shows that by iterating several times lower closure operators the approximation of the fixpoint may be improved. Given a correct abstraction ρ of ρ , the limit Yδ of the sequence of the narrowing operator, Y0 = X , Yi+1 = Yi ρ (Yi ) is an abstraction of (ρ ◦ γ)(X ). Note that even if ρ is not an optimal abstraction of ρ , Yδ may be significantly more precise than ρ (X ). A relevant application is the analysis of complex test conjunction C1 ∧ · · · ∧ Cp , where each atomic test Ci is modeled in the abstract as ρi .

Vn be the variables on finite ˆ i , and C a constraint. The value discrete domains D1 . . Dn , Di ⊆ D xi ∈ Di has a support if and only if ∀j ∈ 1, n , j = i, ∃xj ∈ Dj such that C(x1 , . . , xn ) is true. The most usual consistencies are given in the following. – Given variables v1 . . vn on finite discrete ˆ i , and C a constraint. The domains are domains D1 . . Dn , Di ⊆ D called GAC for C if and only if ∀i ∈ 1, n , ∀x ∈ Di , x has a support. The GAC only keeps the values for which there is a solution for the constraint C, namely, values having a support.

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.

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Abstract Domains in Constraint Programming by Marie Pelleau


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