descriptionPublicationkeyboard_double_arrow_right Article 13 Dec 2022 English Publisher:Informa UK LimitedJournal:Optimization, volume 73, pages 1,253-1,266 (issn: 0233-1934, eissn: 1029-4945,

Authors: Freixas Bosch, Josep;

doi: 10.1080/02331934.2022.2154126

handle: 2117/382121

On the enumeration of some inequivalent monotone Boolean functions

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Abstract

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.

This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization on 13 Dec 2022, available at: http://www.tandfonline.com/10.1080/02331934.2022.2154126.

This publication is part of the I+D+i project/PID2019-104987GB-I00, financed by MCIN/AEI/10.13039/501100011033/; Spanish Ministry of Science and Innovation.

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Keywords

Classificació AMS::91 Game theory, economics, social and behavioral sciences::91B Mathematical economics, recurrence relations, Classificació AMS::65 Numerical analysis::65Q05 Difference and functional equations, recurrence relations, social and behavioral sciences::91B Mathematical economics, Enumeration of Boolean functions, Enumeration of tripartite and quadripartite simple games, Simple games, Inequivalent monotone Boolean functions, Dedekind numbers, Algebra, Boolean, social and behavioral sciences::91A Game theory, series, Jocs, Teoria de, Game theory, Classificació AMS::91 Game theory, economics, social and behavioral sciences::91A Game theory, Teoria de, Classificació AMS::91 Game theory, Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs, economics, Jocs, Classificació AMS::65 Numerical analysis::65Q05 Difference and functional equations, Classificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science, Algebra, Classificació AMS::40 Sequences, summability::40B05 Multiple sequences and series, Boolean, Àlgebra booleana, Classificació AMS::40 Sequences, series, summability::40B05 Multiple sequences and series

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