Phase transitions and the search problem

Techniques that were originally developed in statistical mechanics can be applied to search problems that arise commonly in artificial intelligence and predict that abrupt changes in computational cost should occur universally, as heuristic effectiveness or search space topology is varied.

Abstract

We describe how techniques that were originally developed in statistical mechanics can be applied to search problems that arise commonly in artificial intelligence. This approach is useful for understanding the typical behavior of classes of problems. In particular, these techniques predict that abrupt changes in computational cost, analogous to physical phase transitions, should occur universally, as heuristic effectiveness or search space topology is varied. We also present a number of open questions raised by these studies.