GAC Via Unit Propagation

In this paper we argue that an attractive and potentially very general way of achieving generalized arc consistency (GAC) on a constraint is by using unit propagation (UP) over a CNF encoding of the constraint. This approach to GAC offers a number of advantages over traditional constraint specific algorithms (propagators): it is easier to implement, it automatically provides incrementality and decrementality in a backtracking context, and it can provide clausal reasons to support learning and non-chronological backtracking. Although UP on standard CNF encodings of a constraint fails to achieve GAC, we show here that alternate CNF encodings can be used on which UP does achieve GAC. We provide a generic encoding applicable to any constraint. We also give structure specific encodings for the regular, among, and gen-sequence constraints on which UP can achieve GAC with the same run time bounds as previously presented propagators. Finally, we explain how a UP engine can be added to a CSP ...

• Type: Conference
• Year: 2007
• Where: CP
• Authors: Fahiem Bacchus
• Keywords: Cnf Encodings, Constraint Specific Algorithms, CP 2007, Programming Languages, Traditional Constraint Specific