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

URN to cite this document: urn:nbn:de:bvb:703-epub-3246-3

Title data

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.

Further data

Item Type: Preprint, postprint
Keywords: switching functions; Boolean functions; linear separability problem; threshold functions; asummability conditions; simple games
Subject classification: Mathematics Subject Classification Code: 06E30 91A12 (68T27 92B20 94C10)
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Profile Fields > Emerging Fields > Governance and Responsibility
Faculties
Profile Fields
Profile Fields > Emerging Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3246-3
Date Deposited: 20 Mar 2017 09:36
Last Modified: 18 Mar 2019 14:14
URI: https://epub.uni-bayreuth.de/id/eprint/3246

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