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 adequate to resolve huge commercial difficulties, in a ordinary framework. although, solvers are devoted to a unmarried variable sort: integer or actual. fixing combined difficulties depends on advert hoc modifications. In one other box, summary Interpretation bargains instruments to turn out application 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 variety of representations for those abstractions were proposed. they're known 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 a view to construct a common fixing technique, facing either integer and actual variables. We additionally examine the octagons summary area, already outlined in summary Interpretation. Guiding the quest via the octagonal relatives, we receive sturdy effects on a continual benchmark. We additionally outline our fixing process utilizing summary Interpretation thoughts, which will contain current summary domain names. Our solver, AbSolute, is ready to remedy 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 able to dealing with virtually all summary domains
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Extra resources for Abstract Domains in Constraint Programming
2. Constraint programming CP was introduced by Montanari [MON 74] in 1974. It relies on the idea that combinatorial problems can be expressed as a conjunction of ﬁrst-order logic formulas, called constraints. A problem is called combinatorial when it contains a very large number of combinations of possible values. Take the example of a Sudoku puzzle: each cell that does not already have a value can take the value between 1 and 9. The number of all the possible grids, corresponding to the enumeration of all the possible values for all the empty boxes, is very large.
C8 ) to the columns and (C9 . . C12 ) to the blocks: 28 Abstract Domains in Constraint Programming C1 : alldiﬀerent(v1 , v2 , v3 , v4 ) C5 : alldiﬀerent(v1 , v5 , v9 , v13 ) C6 : alldiﬀerent(v2 , v6 , v10 , v14 ) C2 : alldiﬀerent(v5 , v6 , v7 , v8 ) C3 : alldiﬀerent(v9 , v10 , v11 , v12 ) C7 : alldiﬀerent(v3 , v7 , v11 , v15 ) C4 : alldiﬀerent(v13 , v14 , v15 , v16 ) C8 : alldiﬀerent(v4 , v8 , v12 , v16 ) C9 : alldiﬀerent(v1 , v2 , v5 , v6 ) C10 : alldiﬀerent(v3 , v4 , v7 , v8 ) C11 : alldiﬀerent(v9 , v10 , v13 , v14 ) C12 : alldiﬀerent(v11 , v12 , v15 , v16 ) Solutions of this CSP correspond to all the Sudoku grids properly ﬁlled.
In contrast, CP integrates for continuous domains an explicit deﬁnition of accuracy. The choice of abstract domain in a CP solver does not change its precision (which is ﬁxed), but its efﬁciency (the amount of computation needed to achieve the desired accuracy). 50 Abstract Domains in Constraint Programming Another signiﬁcant difference is that all the techniques in AI are parameterized by abstract domains. On the contrary, CP solvers are highly dependent on the variables type (integer or real) and are especially dedicated to one domain representation.