On the enumeration of Boolean functions with distinguished variables

Abstract

Boolean functions have a fundamental role in neural networks and machine learning. Enumerating these functions and significant subclasses is a highly complex problem. Therefore, it is of interest to study subclasses that escape this limitation and can be enumerated by means of sequences depending on the number of variables. In this article, we obtain seven new formulas corresponding to enumerations of some subclasses of Boolean functions. The versatility of these functions does the problem interesting to several different fields as game theory, hypergraphs, reliability, cryptography or logic gates.