On the violation of circuits in decomposable negation normal form

Authors:
Lucas Bordeaux;Nina Narodytska
Affiliations:
Microsoft Research Cambridge, UK;NICTA and University of NSW, Sydney, Australia
Venue:
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
Year:
2012

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Abstract

Local Search approaches to constraint satisfaction are based on the ability to compute violation scores. These estimate 'how far' a given assignment is from satisfying the constraints, and aim at guiding the search towards assignments whose violation will, ultimately, be null. We study the computation of violation functions for Boolean predicates encoded in Decomposable Negation Normal Form, an important class of logical circuits that encode interesting constraints. We show that for these circuits an elegant and efficient violation function first proposed by Z. Stachniak is "ideal" in a certain sense. We discuss more broadly the notion of "ideal" violation and discuss the implications of this result.