Download Abstract Domains in Constraint Programming by Marie Pelleau PDF

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 business difficulties, in a usual framework. despite the fact that, solvers are devoted to a unmarried variable variety: integer or actual. fixing combined difficulties will depend on advert hoc differences. In one other box, summary Interpretation bargains instruments to turn out 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 variety of 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 symbolize family among the variables.

In this paintings, we outline summary domain names for Constraint Programming, so one can construct a everyday fixing procedure, facing either integer and genuine variables. We additionally examine the octagons summary area, already outlined in summary Interpretation. Guiding the hunt through the octagonal kin, we receive sturdy effects on a continuing benchmark. We additionally outline our fixing approach utilizing summary Interpretation thoughts, so as to comprise latest summary domain names. Our solver, AbSolute, is ready to clear up combined difficulties and use relational domains.

  • Exploits the over-approximation easy methods 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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Sample text

CP combines the constraints on any type of variables and sometimes loses efficiency to gain expressiveness. 2 Abstract Interpretation for the Constraints In this chapter we give unified definitions for the different components of the resolution process in constraint programming (CP). With these new definitions, a unique resolution method can be defined for any abstract domain. This new resolution scheme no longer depends on the type of the variables. Moreover, the definition of the abstract domains in CP gives the possibility of solving problems using non-Cartesian domain representations.

The best-known solvers are Declic [BEN 97a], Numerica [HEN 97], RealPaver [GRA 06] and Ibex [CHA 09a]. 0 [PRU 14, FAG 14], which incorporate both a discrete and a continuous solver. Implementation tricks are needed to solve problems containing both integer and real variables. In the following, we use the terms “mixed problem” or “continuous-discrete problem” for this type of problems. If the selected solver is discrete, real variables are discretized, and the possible values for the variables are listed for a given step.

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. – Let v1 and v2 be two integer variables with domains D1 = 0, 2 and D2 = 0, 2 . Let C : v1 + v2 ≤ 3 be a constraint. e. C(2, 0) is true. In contrast, C(2, 2) is false. In the case of real domains, an important feature is that constraints can answer: – true, if the box only contains solutions; – false, if the box contains no solution at all; – maybe, when we cannot determine whether the box contains solutions or not.

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