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...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Optimization Ročník 73; číslo 4; s. 1253 - 1266
Hlavní autor: Freixas, Josep
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Taylor & Francis 02.04.2024
Taylor & Francis LLC
Témata:
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
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2154126