New PDF release: Abstract Domains in Constraint Programming

By Marie Pelleau

ISBN-10: 1785480103

ISBN-13: 9781785480102

Constraint Programming goals at fixing tough combinatorial difficulties, with a computation time expanding in perform exponentially. The equipment are at the present time effective adequate to unravel huge commercial difficulties, in a typical framework. despite the fact that, solvers are devoted to a unmarried variable variety: integer or actual. fixing combined difficulties depends on advert hoc changes. In one other box, summary Interpretation bargains instruments to turn out software homes, via 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 referred to as summary domain names. summary domain names can combine any kind of variables, or even characterize kinfolk among the variables.

In this paintings, we outline summary domain names for Constraint Programming, so that it will construct a customary fixing technique, facing either integer and genuine 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 strategy utilizing summary Interpretation concepts, as a way to contain present summary domain names. Our solver, AbSolute, is ready to resolve combined difficulties and use relational domains.

  • Exploits the over-approximation ways to combine AI instruments within the equipment of CP
  • Exploits the relationships captured to unravel 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

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For the inclusion: ˆ i , a i ≤ bi ai , bi | ∀i, ai , bi ⊆ D IB = ∪∅ i For real variables, as the reals are not computer representable, their domains are represented by floating bounds intervals. – Let v1 , . . , vn be the variables with ˆ 1, . . , D ˆ n ∈ I. We call box any bounded continuous domains D ˆ The boxes in D ˆ Cartesian product of floating bounds intervals in D. 2. Constraint satisfaction For integer variables, given an instantiation for the variables, a constraint answers true if this variables assignment satisfies the constraint, and false otherwise.

Another way to improve the accuracy is to add local iterations [GRA 92]. ). 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.

V16 ) taking their values in ˆ 2 = {3}, D ˆ3 = D ˆ9 = D ˆ 16 = {1}, D ˆ 8 = {4}, D ˆ 10 = the domains D {2}, all the other domains being equal to 1, 4 , and 12 constraints, (C1 . . C4 ) corresponding to the rows, (C5 . . 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.

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Abstract Domains in Constraint Programming by Marie Pelleau

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