ON THE SYNTHESIS OF THRESHOLD DEVICES,
Abstract
A Boolean function of n variables may be defined as a mapping from the vertices of an n-dimensional hypercube to (TRUE, FALSE). A threshold function is defined as a Boolean function whose TRUE vertices are separable from the FALSE vertices by a hyperplane. It is shown that the vertices of the above hypercube lie on the surface of a hypersphere and are distributed uniformly over the surface of this hypersphere. A comparison is made between a threshold function and a continuous threshold function, i. e., the set of points on the surface of the hypersphere which lie on the TRUE side of the hyperplane. Based on this comparison, an approximate threshold device realization for any Boolean function is developed. Further, an algorithm is derived which, starting with the approximation, develops a valid realization if the function is a threshold function. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1963
- Accession Number
- AD0437294
Entities
People
- Philip Kaszerman
Organizations
- New York University