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

Title data

Freixas, Josep ; Freixas, Marc ; Kurz, Sascha:
Characterization of threshold functions : state of the art, some new contributions and open problems.
Bayreuth , 2016 . - 23 p.

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Official URL: Volltext

Abstract in another language

The study of the characterization of threshold functions within the class of switching functions is an important problem that goes back at least to the
mid--20th century. Due to different motivations switching and threshold functions have been investigated in a variety of different mathematical contexts:
Boolean or switching functions, neural networks, hypergraphs, coherent structures, Sperner families, clutters, secret sharing and simple games or binary voting systems.

The paper revises the state of the art about this significant problem and proposes some new contributions concerning asummability and invariant asummability, a
refinement of asummability. It also includes several questions and conjectures for future research whose solution would mean a new breakthrough.

Further data

Item Type: Preprint, postprint, working paper, discussion paper
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)
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
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 05 Mar 2016 22:00
Last Modified: 20 Mar 2017 10:04
URI: https://eref.uni-bayreuth.de/id/eprint/31397

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