By Marie Pelleau

Constraint Programming goals at fixing not easy combinatorial difficulties, with a computation time expanding in perform exponentially. The tools are this day effective sufficient to unravel huge business difficulties, in a favourite framework. in spite of the fact that, solvers are devoted to a unmarried variable variety: integer or genuine. fixing combined difficulties depends on advert hoc modifications. In one other box, summary Interpretation bargains instruments to end up application homes, 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. quite a few 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 signify family members among the variables.

In this paintings, we outline summary domain names for Constraint Programming, as a way 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 by means of the octagonal family, we receive strong effects on a continuing benchmark. We additionally outline our fixing procedure utilizing summary Interpretation strategies, so as to comprise present summary domain names. Our solver, AbSolute, is ready to clear up combined difficulties and use relational domains.

  • Exploits the over-approximation the right way 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 in a position to dealing with virtually all summary domains

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Extra info for Abstract Domains in Constraint Programming

Sample text

In order to define the problem, the user defines the constraints, which are the specifications of the problem. A constraint represents a specific combinatorial relationship of the problem [ROS 06]. With the example of Sudoku, the fact that each number between 1 and 9 appears exactly once in each row is a constraint. Each constraint comes with ad hoc operators using the structure expressed by the constraint to reduce combinatorics. The constraints are then combined into solving algorithms. Most research efforts in CP focus on defining and improving constraints [FAG 11], developing efficient algorithms [BES 11, PET 11] or fine tuning for the solvers [ANS 09, ARB 09].

Moreover, it does not feature any narrowing operator. Although they may not exist, these different operators are useful in order to have only one possible representation for a given concrete domain (abstraction) and to refine the overapproximation while computing the fixpoint (narrowing). 3. Conclusion The previous sections have briefly presented AI. The main definitions and notions needed in the following are given. For a more detailed presentation, the readers are advised to refer to [COU 77a]. To sum up, AI automatically analyzes programs in order to certify that they do not contain any execution errors.

The main definitions and notions needed in the following are given. For a more detailed presentation, the readers are advised to refer to [COU 77a]. To sum up, AI automatically analyzes programs in order to certify that they do not contain any execution errors. This analyzing relies on the computation of the program semantic, the set of all the possible values for the variables of the program. Directly computing the concrete semantics can be very time-consuming in terms of computation time and can even be undecidable.

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