  
  
                             [1X GAP 4 Package Thelma [101X
  
  
                [1X THreshold ELements, Modeling and Applications [101X
  
  
                                     1.0.2
  
  
                                      2018
  
  
                                  Victor Bovdi
  
                                  Vasyl Laver
  
  
  
  Victor Bovdi
      Email:    [7Xmailto:vbovdi@gmail.com[107X
      Address:  [33X[0;14YDepartment of Mathematical Sciences[133X
                [33X[0;14YUAEU[133X
                [33X[0;14YAl Ain, United Arab Emirates[133X
  
  
  Vasyl Laver
      Email:    [7Xmailto:vasyl.laver@uzhnu.edu.ua[107X
      Address:  [33X[0;14YDepartment of Mathematical Sciences[133X
                [33X[0;14YUAEU[133X
                [33X[0;14YAl Ain, United Arab Emirates[133X
  
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2018 by the authors[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2 or higher.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (thelma)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YOverview over this manual[133X
    1.2 [33X[0;0YInstallation[133X
    1.3 [33X[0;0YFeedback[133X
  2 [33X[0;0YBoolean Functions[133X
    2.1 [33X[0;0YBasic Operations[133X
      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
  3 [33X[0;0YThreshold Elements[133X
    3.1 [33X[0;0YBasic Operations[133X
      3.1-1 ThresholdElement
      3.1-2 IsThresholdElement
      3.1-3 OutputOfThresholdElement
      3.1-4 StructureOfThresholdElement
      3.1-5 RandomThresholdElement
      3.1-6 Comparison of Threshold Elements
    3.2 [33X[0;0YSingle Threshold Element Realizability[133X
      3.2-1 CharacteristicVectorOfFunction
      3.2-2 IsCharacteristicVectorOfSTE
      3.2-3 IsInverseInKernel
      3.2-4 IsKernelContainingPrecedingVectors
      3.2-5 IsRKernelBiggerOfCombSum
      3.2-6 BooleanFunctionBySTE
      3.2-7 PDBooleanFunctionBySTE
    3.3 [33X[0;0YIterative Training Methods[133X
      3.3-1 ThresholdElementTraining
      3.3-2 ThresholdElementBatchTraining
      3.3-3 WinnowAlgorithm
      3.3-4 Winnow2Algorithm
      3.3-5 STESynthesis
  4 [33X[0;0YNetworks of Threshold Elements[133X
    4.1 [33X[0;0YBasic Operations[133X
      4.1-1 NeuralNetwork
      4.1-2 IsNeuralNetwork
      4.1-3 OutputOfNeuralNetwork
    4.2 [33X[0;0YNetworks of Threshold Elements[133X
      4.2-1 BooleanFunctionByNeuralNetwork
      4.2-2 BooleanFunctionByNeuralNetworkDASG
  5 [33X[0;0YMulti-Valued Threshold Elements[133X
    5.1 [33X[0;0YThreshold Elements over [22XGF(p^k)[122X[133X
      5.1-1 MVThresholdElement
      5.1-2 IsMVThresholdElement
      5.1-3 OutputOfMVThresholdElement
      5.1-4 StructureOfMVThresholdElement
      5.1-5 MVBooleanFunctionBySTE
  
  
  [32X
