Planning using abstraction induced by substitution property

A knowledge-independent planning approach for a class of structured problems is discussed. The planning method is based on abstraction of the search space. It is shown that if the search space has the substitution property (substitution partitions), then a hierarchy of abstract spaces can be realized in which each space is a homomorphic image of its predecessor. The determination of the substitution property is considered. A sufficient condition for the existence of the substitution partition is identified in the form of a partition generator. Two interesting classes of problems are shown to possess such a generator. They are the problems with symmetry and direct product spaces with acyclic dependency (interaction)