On the enumeration of some inequivalent monotone Boolean functions

This paper considers inequivalent monotone Boolean functions of an arbitrary number of variables, two monotone Boolean functions are equivalent if one can be obtained from the other by permuting the variables. It focuses on some inequivalent  monotone Boolean functions with three and four types of e...

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Bibliographic Details
Published in:Optimization Vol. 73; no. 4; pp. 1253 - 1266
Main Author: Freixas, Josep
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 02.04.2024
Taylor & Francis LLC
Subjects:
Artificial intelligence
Boolean functions
Decision theory
Dedekind numbers
Enumeration
enumeration of Boolean functions
enumeration of tripartite and quadripartite simple games
Equivalence
Game theory
inequivalent monotone Boolean functions
Mathematical analysis
Multiple criterion
Network reliability
Neural networks
simple games
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:This paper considers inequivalent monotone Boolean functions of an arbitrary number of variables, two monotone Boolean functions are equivalent if one can be obtained from the other by permuting the variables. It focuses on some inequivalent  monotone Boolean functions with three and four types of equivalent variables, where the variables are either dominant or dominated. The paper provides closed formulas for their enumeration as a function of the number of variables. The problem we deal with is very versatile since inequivalent monotone Boolean functions are monotonic simple games, structures that are used in many fields such as game theory, neural networks, artificial intelligence, reliability or multiple-criteria decision-making.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2154126