Download this Paper Open PDF in Browser

Characterization of Threshold Functions: State of the Art, Some New Contributions and Open Problems

23 Pages Posted: 2 Mar 2016  

Josep Freixas

Polytechnic University of Catalonia (UPC)

Marc Freixas

Independent

Sascha Kurz

University of Bayreuth

Date Written: March 1, 2016

Abstract

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.

Keywords: switching functions, Boolean functions; linear separability problem; threshold functions; asummability conditions; simple games

JEL Classification: C71

Suggested Citation

Freixas, Josep and Freixas, Marc and Kurz, Sascha, Characterization of Threshold Functions: State of the Art, Some New Contributions and Open Problems (March 1, 2016). Available at SSRN: https://ssrn.com/abstract=2740475 or http://dx.doi.org/10.2139/ssrn.2740475

Josep Freixas (Contact Author)

Polytechnic University of Catalonia (UPC) ( email )

C. Jordi Girona, 31
Barcelona, 08034
Spain

Marc Freixas

Independent

No Address Available

Sascha Kurz

University of Bayreuth ( email )

Universit├Ątsstr. 30
Lehrstuhl f├╝r Wirtschaftsmathematik
Bayreuth, Bavaria D-95440
Germany
+49 921 55 7353 (Phone)
+49 921 55 7352 (Fax)

HOME PAGE: http://www.wm.uni-bayreuth.de/index.php?id=sascha

Paper statistics

Downloads
14
Abstract Views
95