Approximate Methods of Solving Logical Problems

Abstract

In the formulation of logical problems it is frequently required not only that a solution be obtained, but also that this solution be the very best solution, in some sense or other. For example, in synthesizing a logical circuit one might be required to obtain a scheme which not only realizes a given system of Boolean functions, but which at the same time contains a minimal number of elements; in seeking proofs to theorems, one wishes to find not only correct proofs, but also the simplest of the correct proofs; in analyzing chess positions one wishes not only to find a winning sequence of moves, but to choose the most elegant of the winning sequences. In each such problem, it is possible to introduce some quality function, and then seek an exact solution which corresponds to an extremum of the quality function thus introduced.