By Marie Pelleau
Constraint Programming goals at fixing tough combinatorial difficulties, with a computation time expanding in perform exponentially. The equipment are this day effective sufficient to unravel huge commercial difficulties, in a widely used framework. besides the fact that, solvers are devoted to a unmarried variable sort: integer or genuine. fixing combined difficulties depends upon advert hoc modifications. In one other box, summary Interpretation deals instruments to end up 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. 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 signify kin among the variables.
In this paintings, we outline summary domain names for Constraint Programming, with a purpose to construct a wide-spread fixing technique, facing either integer and actual variables. We additionally examine the octagons summary area, already outlined in summary Interpretation. Guiding the hunt via the octagonal kinfolk, we receive stable effects on a continual benchmark. We additionally outline our fixing process utilizing summary Interpretation options, with a view to comprise 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 resolve non-stop difficulties extra effectively
- Learn from the builders of a solver able to dealing with virtually all summary domains
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Extra info for Abstract Domains in Constraint Programming
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 .
In other words, only some characteristics are kept in order to simplify and speed up the process while keeping the process sound. For each concrete operator, an abstract operator is deﬁned and efﬁcient algorithms are designed. The abstract semantic is approximated using an abstract domain. There exist several abstract domains in AI offering different trade-offs between precision and computation time. After this survey of AI general theory and techniques, the next section brieﬂy presents CP, its principles, scientiﬁc challenges and resolution techniques.
This is called the propagation loop. 2. 12), forms ﬁnite complete lattices for inclusion, it is sufﬁcient to compute the consistency for each constraint until the ﬁxpoint is reached. It was demonstrated by Apt in 1999 [APT 99] and Benhamou in 1996 [BEN 96] that the order in which the consistences are applied is irrelevant. Indeed, as the lattices are complete, any subset has a unique least element: the consistent ﬁxpoint. State of the Art 39 However, the order in which the consistencies, and therefore the propagators, are applied inﬂuences the speed of convergence, that is, the number of iterations required to reach the ﬁxpoint.
Abstract Domains in Constraint Programming by Marie Pelleau