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href="chap1.html" >1</a> <a href="chap2.html" >2</a> <a href="chap3.html" >3</a> <a href="chap4.html" >4</a> <a href="chap5.html" >5</a> <a href="chapBib.html" >Bib</a> <a href="chapInd.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0_mj.html" >[MathJax on]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >Thelma</h1 >div >br />Email: <span class="URL" ><a href="mailto:vbovdi@gmail.com" >vbovdi@gmail.com</a></span >br />Address : <br />Department of Mathematical Sciences<br /> UAEU<br /> Al Ain, United Arab Emirates<br br />Email: <span class="URL" ><a href="mailto:vasyl.laver@uzhnu.edu.ua" >vasyl.laver@uzhnu.edu.ua</a></span >br />Address : <br />Department of Mathematical Sciences<br /> UAEU<br /> Al Ain, United Arab Emirates<br "X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>on 2 or higher.</p>"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1.html#X7DFB63A97E67C0A1" >1 <span class="Heading" >Introduction</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X786BACDB82918A65" >1.1 <span class="Heading" >Overview over this manual</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X8360C04082558A12" >1.2 <span class="Heading" >Installation</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap1.html#X80D704CC7EBFDF7A" >1.3 <span class="Heading" >Feedback</span ></a>span >div >div >div class="ContChap" ><a href="chap2.html#X830F6677819A6656" >2 <span class="Heading" >Boolean Functions</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X82EB5BE77F9F686A" >2.1 <span class="Heading" >Basic Operations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7D8A971A84186BF0" >2.1-1 LogicFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7C34DEE27EC3A009" >2.1-2 IsLogicFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X857A4F117BDDF1B6" >2.1-3 PolynomialToBooleanFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X78B9DD8E81EE65A8" >2.1-4 IsUnateInVariable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X8203046F7C97EAFE" >2.1-5 IsUnateBooleanFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7D0DEF0B7E9FE027" >2.1-6 InfluenceOfVariable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X86C000FE831CFEDE" >2.1-7 SelfDualExtensionOfBooleanFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7C09D66E84201A77" >2.1-8 SplitBooleanFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X8108DE5280908841" >2.1-9 KernelOfBooleanFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2.html#X7B1B54877B354F23" >2.1-10 ReducedKernelOfBooleanFunction</a></span >div ></div >div >div class="ContChap" ><a href="chap3.html#X83DFEF607CDA3594" >3 <span class="Heading" >Threshold Elements</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X82EB5BE77F9F686A" >3.1 <span class="Heading" >Basic Operations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X853FF8AC85E5C4CE" >3.1-1 ThresholdElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7E7F95D57EB87BB4" >3.1-2 IsThresholdElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7F293D2D810ADBBB" >3.1-3 OutputOfThresholdElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8116985278C60D33" >3.1-4 StructureOfThresholdElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X800C6898856CD0E9" >3.1-5 RandomThresholdElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7C9E64E17B07DF58" >3.1-6 Comparison of Threshold Elements</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X7DB8E3E87D8AD820" >3.2 <span class="Heading" >Single Threshold Element Realizability</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8351E15B7CCDEB62" >3.2-1 CharacteristicVectorOfFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8502A0827ECF1FFE" >3.2-2 IsCharacteristicVectorOfSTE</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7B0855E28717AF12" >3.2-3 IsInverseInKernel</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X83B234DB7F260879" >3.2-4 IsKernelContainingPrecedingVectors</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7877118A7A9C51CB" >3.2-5 IsRKernelBiggerOfCombSum</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X83D3B18486C5D0B7" >3.2-6 BooleanFunctionBySTE</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8451E4EA7F06222F" >3.2-7 PDBooleanFunctionBySTE</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X7D0584857E0D2265" >3.3 <span class="Heading" >Iterative Training Methods</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X83567B7D79958EBF" >3.3-1 ThresholdElementTraining</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X83CD889E8125E949" >3.3-2 ThresholdElementBatchTraining</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X81FEA8AF80573A12" >3.3-3 WinnowAlgorithm</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X85162EF17EE09E50" >3.3-4 Winnow2Algorithm</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7C4B705884A78907" >3.3-5 STESynthesis</a></span >div ></div >div >div class="ContChap" ><a href="chap4.html#X7BA69E617DE465FE" >4 <span class="Heading" >Networks of Threshold Elements</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X82EB5BE77F9F686A" >4.1 <span class="Heading" >Basic Operations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X780C027786A8E34B" >4.1-1 NeuralNetwork</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X79B24B8F79161064" >4.1-2 IsNeuralNetwork</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7C93C473784D1676" >4.1-3 OutputOfNeuralNetwork</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X7BA69E617DE465FE" >4.2 <span class="Heading" >Networks of Threshold Elements</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X786FB7237D875561" >4.2-1 BooleanFunctionByNeuralNetwork</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7C6E4221828E6609" >4.2-2 BooleanFunctionByNeuralNetworkDASG</a></span >div ></div >div >div class="ContChap" ><a href="chap5.html#X8735CBCC80897D83" >5 <span class="Heading" >Multi-Valued Threshold Elements</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X83640D4B7FFE0F9F" >5.1 <span class="Heading" >Threshold Elements over <span class="SimpleMath" >GF(p^k)</span ></span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X818FF66D7919D8B1" >5.1-1 MVThresholdElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7C4A761F864B8EFA" >5.1-2 IsMVThresholdElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7E64FB7684207AED" >5.1-3 OutputOfMVThresholdElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7B2520F37C18CC81" >5.1-4 StructureOfMVThresholdElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7B103C6B7EB903EF" >5.1-5 MVBooleanFunctionBySTE</a></span >div ></div >div >div class="ContChap" ><a href="chapBib.html" ><span class="Heading" >References</span ></a></div >div class="ContChap" ><a href="chapInd.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0.html" >Top</a> <a href="chap1.html" >1</a> <a href="chap2.html" >2</a> <a href="chap3.html" >3</a> <a href="chap4.html" >4</a> <a href="chap5.html" >5</a> <a href="chapBib.html" >Bib</a> <a href="chapInd.html" >Ind</a> </div >hr />"foot" >generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc " >GAPDoc2HTML</a></p>body >html > 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