Generating abstraction hierarchies

Generating Abstraction Hierarchies presents a completely automated approach to generating abstractions for problem solving. The abstractions are generated using a tractable, domain-independent algorithm whose only inputs are the definition of a problem space and the problem to be solved and whose output is an abstraction hierarchy that is tailored to the particular problem. The algorithm generates abstraction hierarchies that satisfy the `ordered monotonicity' property, which guarantees that the structure of an abstract solution is not changed in the process of refining it. An abstraction hierarchy with this property allows a problem to be decomposed such that the solution in an abstract space can be held invariant while the remaining parts of a problem are solved. The algorithm for generating abstractions is implemented in a system called ALPINE, which generates abstractions for a hierarchical version of the PRODIGY problem solver. Generating Abstraction Hierarchies formally defines this hierarchical problem solving method, shows that under certain assumptions this method can reduce the size of a search space from exponential to linear in the solution size, and describes the imple