An Approach to the General Synthesis of a Threshold Element Network

摘要

This dissertation investigates an approach to the general synthesis of a network with threshold elements using approximating functions called minimal threshold approximations. The minimal threshold approximation or M function of a given switching function is a threshold function having the smallest set of true and false vectors which are false and true vectors respectively of the given switching function. A mixed integer linear programming formulation is given for the determination of M functions. Some of the algebraic properties which hold between a given function and an M function are investigated. A class of less restrictive approximations called T/M and F/M functions is investigated. A synthesis procedure is described for both forms of approximations. A subclass of the class of threshold functions, called simple functions, is investigated. Based on simple functions a test for threshold realizability is given. Finally a procedure is given for synthesizing networks of threshold elements each element of which has a restricted number of inputs. (Author)