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CSL
2009
Springer

Decidable Relationships between Consistency Notions for Constraint Satisfaction Problems

13 years 10 months ago
Decidable Relationships between Consistency Notions for Constraint Satisfaction Problems
Abstract. We define an abstract pebble game that provides game interpretations for essentially all known consistency algorithms for constraint satisfaction problems including arc-consistency, (j, k)-consistency, k-consistency, k-minimality, and refinements of arc-consistency such as peek arc-consistency and singleton arc-consistency. Our main result is any two instances of the abstract pebble game where the first satisfies the additional condition of being stacked, there exists an algorithm to decide whether consistency with respect to the first implies consistency with respect to the second. In particular, there is a decidable criterion to tell whether singleton arc-consistency with respect to a given constraint language implies k-consistency with respect to the same constraint language, for any fixed k. We also offer a new decidable criterion to tell whether arc-consistency implies satisfiability which pulls from methods in Ramsey theory and looks more amenable to generalizat...
Albert Atserias, Mark Weyer
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where CSL
Authors Albert Atserias, Mark Weyer
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