# Accession Number:

## AD0643379

# Title:

## SYNTHESIS PROBLEMS IN LINEAR THRESHOLD LOGIC,

# Descriptive Note:

# Corporate Author:

## MICHIGAN UNIV ANN ARBOR SYSTEMS ENGINEERING LAB

# Personal Author(s):

# Report Date:

## 1966-06-01

# Pagination or Media Count:

## 147.0

# Abstract:

A study was made of several problems associated with networks of threshold elements. First a test for linear separability is presented, then the problem of two-level threshold minimization is treated and finally, the synthesis of universal networks is studied. The test for linear separability operates on the inequalities eliminating one at a time, but this is implemented by manipulating the coordinates of a pair of points at a time instead of working on the inequalities themselves. The synthesis of networks of threshold elements which are not limited as to the number of inputs or weights acceptable is treated in this research in two different aspects. The first covers the standard type of network which implements a given function. It is shown that any switching function can be realized by means of a two-level network if both the assertion and negation of the variables are available. A procedure to obtain the minimum network in the sense of requiring the smallest number of threshold elements is also given. The second type of network discussed is a universal network in the sense that any switching function of n variables can be implemented by the network without modifying the connections by simply readjusting the weights and thresholds. Several procedures to minimize different parameters, as total number of elements, maximum number of inputs per element, etc. are discussed. The conclusion is that it is entirely practical to build an adjustable universal network for as many as ten variables. Author

# Descriptors:

# Subject Categories:

- Computer Systems