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Thelma

THreshold ELements, Modeling and Applications

1.3

3 March 2022

Victor Bovdi
Email: vbovdi@gmail.com
Address:
Department of Mathematical Sciences
UAEU
Al Ain, United Arab Emirates

Vasyl Laver
Email: vasyl.laver@uzhnu.edu.ua
Address:
Department of Mathematical Sciences
UAEU
Al Ain, United Arab Emirates

Copyright

© 2018 by the authors

This package may be distributed under the terms and conditions of the GNU Public License Version 2 or higher.

Contents

1.1 Overview over this manual

1.2 Installation

2 Boolean Functions

2.1 Basic Operations

  2.1-1 LogicFunction
  2.1-2 IsLogicFunction
  2.1-3 PolynomialToBooleanFunction
  2.1-4 IsUnateInVariable
  2.1-5 IsUnateBooleanFunction
  2.1-6 InfluenceOfVariable
  2.1-7 SelfDualExtensionOfBooleanFunction
  2.1-8 SplitBooleanFunction
  2.1-9 KernelOfBooleanFunction
  2.1-10 ReducedKernelOfBooleanFunction

4 Networks of Threshold Elements

4.1 Basic Operations

  4.1-1 NeuralNetwork
  4.1-2 IsNeuralNetwork
  4.1-3 OutputOfNeuralNetwork

4.2 Networks of Threshold Elements

4.2-1 BooleanFunctionByNeuralNetwork
4.2-2 BooleanFunctionByNeuralNetworkDASG

5 Multi-Valued Threshold Elements

5.1 Threshold Elements over GF(p^k)

  5.1-1 MVThresholdElement
  5.1-2 IsMVThresholdElement
  5.1-3 OutputOfMVThresholdElement
  5.1-4 StructureOfMVThresholdElement
  5.1-5 MVBooleanFunctionBySTE

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