The role of commutativity in constraint propagation algorithms

Constraint propagation algorithms form an important part of most of the con straint programming systems. We provide here a simple, yet very general fra mework that allows us to explain several constraint propagation algorithms in a systematic way. In this framework we proceed in two steps. First, we i ntroduce a generic iteration algorithm on partial orderings and prove its c orrectness in an abstract setting. Then we instantiate this algorithm with specific partial orderings and functions to obtain specific constraint prop agation algorithms. In particular, using the notions commutativity and semi -commutativity, we show that the AC-3, PC-2, DAC, and DPC algorithms for ac hieving (directional) are consistency and (directional) path consistency ar e instances of a single generic algorithm. The work reported here extends a nd simplifies that of Apt [1999a].