Phase transitions and coarse-grained search

Abstraction is a method for solving a variety of computational search problems that uses coarse-graining to simplify the search. When a coarse-grained, or abstract, solution is found, it is then refined to give a complete solution. We present a model of this abstraction process for constraint satisfaction problems, a well-known class of NP-complete search problems. This model is then used to identify phase transition-like behavior in the effectiveness of abstraction, as well as to determine the type of abstraction that is likely to be most useful for relatively hard instances of these search problems.<>