Arc-Consistency + Unit Propagation = Lookahead

Abstract

Arc-consistency has been one of the most popular consistency techniques for space pruning in solving constraint satisfaction problems (CSPs), while lookahead appears to be its counterpart in answer set solvers. In this paper, we perform a theoretical comparison of their pruning powers, based on the translation of Niemela from CSPs to answer set programs. Especially, we show two results. First, we show that lookahead is strictly stronger than arc-consistency. The extra pruning power comes from the ability to propagate unique values for variables, also called unit propagation in this paper, so that conflicts may be detected. This suggests that arc-consistency can be enhanced with unit propagation for CSPs. We then formalize this technique and show that, under the translation of Niemelä, it has exactly the same pruning power as lookahead. © Springer-Verlag 2004.