Download Abstract Domains in Constraint Programming by Marie Pelleau PDF

By Marie Pelleau

Constraint Programming goals at fixing demanding combinatorial difficulties, with a computation time expanding in perform exponentially. The equipment are at the present time effective sufficient to resolve huge commercial difficulties, in a widespread framework. besides the fact that, solvers are devoted to a unmarried variable style: integer or actual. fixing combined difficulties is dependent upon advert hoc alterations. In one other box, summary Interpretation bargains instruments to turn out software houses, 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 number of representations for those abstractions were proposed. they're referred to as summary domain names. summary domain names can combine any form of variables, or even signify relatives among the variables.

In this paintings, we outline summary domain names for Constraint Programming, so one can construct a commonly used fixing process, facing either integer and actual variables. We additionally learn the octagons summary area, already outlined in summary Interpretation. Guiding the quest through the octagonal family, we receive sturdy effects on a continual benchmark. We additionally outline our fixing approach utilizing summary Interpretation suggestions, that allows you to comprise 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 unravel non-stop difficulties extra effectively
  • Learn from the builders of a solver able to dealing with essentially all summary domains

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Example text

This consistency is also known as hyper-arc consistency or domains consistency [MAC 77b]. – Let (v1 , v2 ) be two variables on discrete domains D1 = D2 = {−1, 0, 1, 2, 3, 4} and v1 = 2v2 + 2 be a constraint. The arc-consistent domains for this CSP are D1 = {0, 2, 4} and D2 = {−1, 0, 1}. Values −1 and 1 have been removed from v1 domain because there exists no value for v2 such that the constraint is satisfied. Similarly, if v2 ≥ 2, we can deduce that v1 ≥ 6. However, the maximum value for v1 is 4.

Indeed, the widening allows an approximation of the least fixpoint to be computed even if the partially ordered set has an infinite increasing chain. So, if the result obtained by the widening meets the given specifications, then the considered program is sound. However, if the result obtained with the widening does not meet the specifications, this does not mean that the program is not sound. This can be due to a too large overapproximation. Therefore, it is mandatory for the widening to be properly designed to minimize the overapproximation and thus avoid false alarms.

Some major domains, such as polyhedra, do not feature any. This difference of interest between the widening and the narrowing may be explained by three facts: first, narrowings are not necessary to achieve soundness unlike widenings which are mandatory. Indeed, the widening allows an approximation of the least fixpoint to be computed even if the partially ordered set has an infinite increasing chain. So, if the result obtained by the widening meets the given specifications, then the considered program is sound.

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