POLYFACT is a learning program that attempts to factor multivariable polynomials. The program has been successful in factoring polynomials (in simplified form) with a maximum of 84 terms, each term consisting of as many as five variables and a maximum degree of 67. The complexity of this learning task placed unusual requirements on the…

A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and…

A proposed student model consisting of a set of programs to represent the student's knowledge state. Teaching proceeds after a comparative evaluation of student and teacher programs, and learning is represented by direct modification of the student model. The advantages of an explicit procedural model are illustrated by considering a program which…

A basic unsolved problem in science is that of understanding learning, the process by which people and machines use their experience in a situation to guide future action in similar situations. The ideas of Piaget, Pavlov, Hull, and other learning theorists, as well as previous heuristic programing models of human intelligence, stimulated this…