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Ouvrages Année : 2011

Constraint resolution theories

Denis Berthier
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Résumé

"Constraint Resolution Theories" introduces a pure logic (non algorithmic) perspective of the finite Constraint Satisfaction Problem (CSP), with emphasis on finding the "simplest" solution. Based on constructive logic, the resolution paradigm relies on the notion of a resolution rule: a logical formula in the condition-action form, where the condition is a pattern that has to be present in the current resolution state to justify the elimination of a candidate (i.e. a possible value of a CSP variable) in the action part. Defining a resolution theory as a fixed set of resolution rules, the book introduces several increasing sequences of such theories. Each of them carries its own notion of simplicity and allows to define a rating of CSP instances; it satisfies two main theorems: the confluence property (guaranteeing that the associated rating has good computational properties) and a correspondence with a form of structured search procedure without guessing (Trial-and-Error). The book includes a detailed case study of Sudoku with: counter-examples to questions about rules subsumption; unbiased statistics and classification results for the rating of instances; scope comparisons for various resolution theories. Other examples from n-Queens show that the same abstract pattern can appear in various guises in different CSPs.
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Dates et versions

hal-02413964 , version 1 (16-12-2019)

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  • HAL Id : hal-02413964 , version 1

Citer

Denis Berthier. Constraint resolution theories. Lulu.com, pp.305, 2011, 978-1-4478-6888-0. ⟨hal-02413964⟩
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