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 tools are this day effective sufficient to unravel huge business difficulties, in a established framework. in spite of the fact that, solvers are devoted to a unmarried variable variety: integer or actual. fixing combined difficulties is determined by advert hoc differences. In one other box, summary Interpretation bargains instruments to end up software houses, via 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 kinfolk among the variables.

In this paintings, we outline summary domain names for Constraint Programming, which will construct a commonly used fixing process, facing either integer and genuine variables. We additionally research the octagons summary area, already outlined in summary Interpretation. Guiding the hunt by means of the octagonal kin, we receive strong effects on a continual benchmark. We additionally outline our fixing technique utilizing summary Interpretation suggestions, as a way to comprise latest summary domain names. Our solver, AbSolute, is ready to clear up 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 in a position to dealing with essentially all summary domains

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Extra info for Abstract Domains in Constraint Programming

Example text

On the contrary, the bound-consistent domain D1 = 0, 4 for the variable v1 is a more compact representation than the arc-consistent domain D1 = {0, 2, 4} but contains more values for v1 . State of the Art 35 Intuitively, we can say that the complexity of computing the bound consistency for a binary constraint is in the worst case O(d2 ) with d the maximum domains size. Indeed, in the worst case, the bound consistency keeps only one value in the domains. Thus, it has to check whether each value has a support.

Eugene C. Freuder [FRE 97]. 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.

Compute the exact set of solutions. This is generally impossible on continuous domains given that the reals are not computer representable, and we usually withdraw either soundness (most of the time) or completeness. In the first case, the resolution returns boxes that may contain points that are not solutions [BEN 99]; we speak of outer approximation or overapproximation. This approximation is the most common. For most 32 Abstract Domains in Constraint Programming problems, we seek to know all the answers, and more importantly we want to be sure not to lose any.

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Abstract Domains in Constraint Programming by Marie Pelleau

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