# Accession Number:

## AD0276717

# Title:

## ENUMERATION OF REGULAR TRUTH FUNCTIONS

# Descriptive Note:

# Corporate Author:

## LOCKHEED MISSILES AND SPACE CO SUNNYVALE CALIF

# Personal Author(s):

# Report Date:

## 1961-03-01

# Pagination or Media Count:

## 1.0

# Abstract:

IN A PREVIOUS WORK, Lockheed Missiles and Space Company, 6-90-61-26, Jan 1961 the classification problem of the linearly separable truth functions was reduced to the enumeration of some special kind of linearly separable truth functions called canonical truth functions. A canonical truth function F of n variables has an important property if x F and y x in the canonical partial order of Qn, then y F. Any truth function F of n variables which has this property is called a regular truth function. Thus, every canonical truth function is regular. One of our intermediate objectives is to answer the question whether or not the converse of this result is true. In a previous work, Lockheed Missiles and Space Company, LMSD-703024, July 1960 it has been shown that every regular truth function of dimension not greater than 5 is linearly separable and hence canonical. Therefore, one may expect that the answer to this question is probably affirmative. However, when the dimension increases, the complexity multiplies and counter examples may turn up. The present work, concerns the problem of counting the regular truth functions as a part of the classification problem. Author