Partitioning 1-variable Boolean functions for various classification of n-variable Boolean functions

Abstract

This paper addresses all possible equivalence classes of 1-variable Boolean functions and from these classes using recursion and Cartesian product of sets, 15 different ways of classifications of n-variable Boolean functions are obtained. The properties with regard to the size and the number of classes for these 15 different ways are also elaborated.

Keywords:

• integer partition
• affine Boolean function
• truth table
• classification
• carry value transformation
• XOR operation
• Hamming distance

2005 AMS Subject Classifications::

• 06E30
• 94C10
• 94A60