On the enumeration of Boolean functions with distinguished variables

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...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Vol. 25; no. 19; pp. 12627 - 12640
Main Author: Freixas, Josep
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021
Subjects:
Artificial Intelligence
Computational Intelligence
Control
Engineering
Focus
Mathematical Logic and Foundations
Mechatronics
Robotics
Complete games
Boolean functions
Enumeration of Boolean functions
Dedekind’s problem
2-Monotonic Boolean functions
Simple games
ISSN:1432-7643, 1433-7479
Online Access:Get full text
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Summary: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.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-020-05422-5