GAP (thelma) - Chapter 1: Introduction

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1 Introduction
1.1 Overview over this manual
1.2 Installation
1.3 Feedback

### 1 Introduction

Thelma stands for ``THreshold ELements, Modelling and Applications". This package is dedicated to realization of Boolean functions by the means of the threshold elements and multilayered perceptrons. Threshold elements were introduced in [MP43]. A certain number of articles on threshold logic appeared in 60-s and 70-s, however this field is regaining a considerable interest nowadays as well (see [HST16],[Hor94], [GVKB11], [KYSV16], e.t.c).

We mostly refer to the methods proposed in [ABGG80], [GPR83], [GMB17], and [Der65].

#### 1.1 Overview over this manual

Chapter 3 describes the functions operating with the threshold elements. They include the basic operations, the functions that verify the realizability of a given Boolean function by a single threshold element, and some iterative methods. Chapter 4 describes the functions for neural networks, built from the threshold elements.

#### 1.2 Installation

To get the newest version of this GAP 4 package download the archive file `thelma-x.x.tar.gz` and unpack it in a directory called "`pkg`", preferably (but not necessarily) in the "`pkg`" subdirectory of your GAP 4 installation. It creates a subdirectory called "`thelma`".

As Thelma has no additional C libraries, there is no need in any additional installation steps.

#### 1.3 Feedback

For bug reports, feature requests and suggestions, please use the github issue tracker at https://github.com/gap-packages/Thelma/issues.

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