On the co-absence of input terms in higher order neuron representation of boolean functions

Name: On the co-absence of input terms in higher order neuron representation of boolean functions
Author: Yapar, O., Öztop, Erhan

İsim	On the co-absence of input terms in higher order neuron representation of boolean functions
Yazar	Yapar, O., Öztop, Erhan
Basım Tarihi:	2017
Basım Yeri	- Springer International Publishin
Konu	Boolean function, Higher order neuron, Sigma-pi neuron model, Polynomial sign representation, Weight elimination, Minimum fan-in representation
Tür	Belge
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	2-s2.0-85021720828
Kayıt Numarası	b4ae00a8-6bae-4376-a36d-930bbc7c4137
Lokasyon	Computer Science
Tarih	2017
Notlar	Due to copyright restrictions, the access to the full text of this article is only available via subscription.
Örnek Metin	Boolean functions (BFs) can be represented by using polynomial functions when −1 and +1 are used represent True and False respectively. The coefficients of the representing polynomial can be obtained by exact interpolation given the truth table of the BF. A more parsimonious representation can be obtained with so called polynomial sign representation, where the exact interpolation is relaxed to allow the sign of the polynomial function to represent the BF value of True or False. This corresponds exactly to the higher order neuron or sigma-pi unit model of biological neurons. It is of interest to know what is the minimal set of monomials or input lines that is sufficient to represent a BF. In this study, we approach the problem by investigating the (small) subsets of monomials that cannot be absent as a whole from the representation of a given BF. With numerical investigations, we study low dimensional BFs and introduce a graph representation to visually describe the behavior of the two-element monomial subsets as to whether they cannot be absent from any sign representation. Finally, we prove that for any n-variable BF, any three-element monomial set cannot be absent as a whole if and only if all the pairs from that set has the same property. The results and direction taken in the study may lead to more efficient algorithms for finding higher order neuron representations with close-to-minimal input terms for Boolean functions.
DOI	10.1007/978-3-319-59081-3_43
Cilt	10262

Kaynağa git Özyeğin Üniversitesi

Aramaya Dön

Özyeğin Üniversitesi

Kaynağa git

On the co-absence of input terms in higher order neuron representation of boolean functions

Yazar Yapar, O., Öztop, Erhan

Basım Tarihi 2017

Basım Yeri - Springer International Publishin

Konu Boolean function, Higher order neuron, Sigma-pi neuron model, Polynomial sign representation, Weight elimination, Minimum fan-in representation

Tür Belge

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 2-s2.0-85021720828

Kayıt Numarası b4ae00a8-6bae-4376-a36d-930bbc7c4137

Lokasyon Computer Science

Tarih 2017

Notlar Due to copyright restrictions, the access to the full text of this article is only available via subscription.

Örnek Metin Boolean functions (BFs) can be represented by using polynomial functions when −1 and +1 are used represent True and False respectively. The coefficients of the representing polynomial can be obtained by exact interpolation given the truth table of the BF. A more parsimonious representation can be obtained with so called polynomial sign representation, where the exact interpolation is relaxed to allow the sign of the polynomial function to represent the BF value of True or False. This corresponds exactly to the higher order neuron or sigma-pi unit model of biological neurons. It is of interest to know what is the minimal set of monomials or input lines that is sufficient to represent a BF. In this study, we approach the problem by investigating the (small) subsets of monomials that cannot be absent as a whole from the representation of a given BF. With numerical investigations, we study low dimensional BFs and introduce a graph representation to visually describe the behavior of the two-element monomial subsets as to whether they cannot be absent from any sign representation. Finally, we prove that for any n-variable BF, any three-element monomial set cannot be absent as a whole if and only if all the pairs from that set has the same property. The results and direction taken in the study may lead to more efficient algorithms for finding higher order neuron representations with close-to-minimal input terms for Boolean functions.

DOI 10.1007/978-3-319-59081-3_43

Cilt 10262