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 implementation of this method in
PRODIGY. The abstractions generated by ALPINE are tested in
multiple domains on large problem sets and are shown to produce
shorter solutions with significantly less search than problem
solving without using abstraction. Generating Abstraction
Hierarchies will be of interest to researchers in machine learning,
planning and problem reformation.
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