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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Vydáno v:Soft computing (Berlin, Germany) Ročník 25; číslo 19; s. 12627 - 12640
Hlavní autor: Freixas, Josep
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021
Témata:
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
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Shrnutí: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