Reformation from State Space to Reduction Space

Abstract

This chapter explores the problem relating to automatically shifting from one problem representation to another representation that is more efficient, with respect to a given problem solving method and a given problem class. A system's ability to solve problems, answer questions, or acquire knowledge has always been bounded by the problem representation initially given to the system. These systems can only perform efficiently to the extent that their problem representations are relevant to the problem at hand. One solution to this dilemma is to develop systems with the ability to alter their problem representation automatically. As a problem solving system changes and improves, its problem representations should also be altered to fit this new situation. The study of shifts of representation can be decomposed into two main aspects: (1) exploring various representations and the shifts between them and (2) the search through this space of representations to discover the ones that will be better for certain problem classes and the reason for them being better. The primitive representation shifts discussed by Amarel (Amarel, 1968) allows for the development of a basic model to derive shifts of representation from an analysis of the state space representation for a single example problem from a given problem class.