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Characterization of threshold functions : state of the art, some new contributions and open problems

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Freixas, Josep ; Freixas, Marc ; Kurz, Sascha:
Characterization of threshold functions : state of the art, some new contributions and open problems.
Bayreuth , 2017 . - 26 S.

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Abstract

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in
threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead
and some new results have been obtained for the problem in the last two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures
for future research.The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal
winning coalitions.

Weitere Angaben

Publikationsform: Preprint, Postprint, Working paper, Diskussionspapier
Keywords: switching functions; Boolean functions; linear separability problem; threshold functions; asummability conditions; simple games
Fachklassifikationen: Mathematics Subject Classification Code: 06E30 91A12 (68T27 92B20 94C10)
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Wirtschaftsmathematik
Profilfelder > Emerging Fields > Governance and Responsibility
Fakultäten
Profilfelder
Profilfelder > Emerging Fields
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 000 Informatik,Informationswissenschaft, allgemeine Werke > 004 Informatik
500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 20 Mär 2017 10:05
Letzte Änderung: 20 Mär 2017 10:40
URI: https://eref.uni-bayreuth.de/id/eprint/36604

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