By Marie Pelleau
Constraint Programming goals at fixing challenging combinatorial difficulties, with a computation time expanding in perform exponentially. The tools are this day effective adequate to unravel huge business difficulties, in a typical framework. even though, solvers are devoted to a unmarried variable style: integer or genuine. fixing combined difficulties depends upon advert hoc variations. In one other box, summary Interpretation bargains instruments to end up software 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. a variety 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 symbolize family members among the variables.
In this paintings, we outline summary domain names for Constraint Programming, with a view to construct a widespread fixing strategy, facing either integer and genuine variables. We additionally research the octagons summary area, already outlined in summary Interpretation. Guiding the quest via the octagonal relatives, we receive stable effects on a continuing benchmark. We additionally outline our fixing approach utilizing summary Interpretation strategies, so one can comprise current 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 in a position to dealing with essentially all summary domains
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Extra info for Abstract Domains in Constraint Programming
It chooses the variable with the smallest domain. The idea is as follows: the earlier one fails, the bigger is the subtree cut in the search tree. To succeed, try ﬁrst where you are most likely to fail –Robert M. Haralick and Gordon L. Elliott [HAR 79]. 6 shows that the earlier the failure appears in the search tree, the bigger is the subtree cut from the search tree. 6(a), failure occurs later and only a small subtree in the search tree is cut. 6(b), failure occurs earlier and a larger subtree in the search tree is cut.
Comparison between the strategy instantiating variables with the biggest domains ﬁrst a) and the ﬁrst-fail strategy b) 46 Abstract Domains in Constraint Programming Once the variable to instantiate is chosen, we need to choose to which value it should be instantiated. Here too, many strategies have been developed, choosing the value maximizing the number of possible solutions [DEC 87, KAS 04], the product of the domains size (promise) [GIN 90] and the sum of the domains size (min-conﬂicts) [FRO 95].
A series of decreasing iterations is applied several times. This method is detailed in the next section. 5. Local iterations The abstract transfer function F (α ◦ F ◦ γ) does not always compute efﬁciently the smallest abstract domain containing the considered expression, even though when it is optimal (γ ◦ F ◦ α) = F . To efﬁciently compute the result of the transfer functions, transfer functions often involve lower closure operators [GRA 92]. – An operator ρ : D → D is a lower closure operator if and only if ρ is: 1) monotonic, ∀X, Y ∈ D, X 2) reductive, ∀X ∈ D, ρ(X) Y ⇒ ρ(X) X; 3) idempotent, ∀X ∈ D, ρ(X) = (ρ ◦ ρ)X.