Research Article Memristive Perceptron for Combinational

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 625790 7 pageshttpdxdoiorg1011552013625790

Research ArticleMemristive Perceptron for Combinational Logic Classification

Lidan Wang Meitao Duan and Shukai Duan

School of Electronic and Information Engineering Southwest University Chongqing 400715 China

Correspondence should be addressed to Shukai Duan duanskswueducn

Received 1 February 2013 Accepted 22 April 2013

Academic Editor Chuandong Li

Copyright copy 2013 Lidan Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The resistance of the memristor depends upon the past history of the input current or voltage so it can function as synapse inneural networks In this paper a novel perceptron combined with the memristor is proposed to implement the combinational logicclassification The relationship between the memristive conductance change and the synapse weight update is deduced and thememristive perceptron model and its synaptic weight update rule are explored The feasibility of the novel memristive perceptronfor implementing the combinational logic classification (NAND NOR XOR and NXOR) is confirmed by MATLAB simulation

1 Introduction

Artificial neural network is a simplification system whichsimulates the organization structure the processing methodand the system function of biological neural system [1] Itdraws a strong attraction to many researchers because ofits performance such as the parallel processing distributedstorage self-learning self-adapting and high fault tolerance[2] Perceptron is the simplest kind of neural network whichcan implement basic learning and parallel processing It iswidely studied to solve the classification problems of medicalimage [3] text [4] mode [5 6] and fingerprint [7] Alarge number of biological synapses respond to receivedsignals to store a series of continuous weights so it is hardto realize perceptron by hard circuits Memristor a newcircuit component in electronics field is suitably used assynapse in neural networks because of its nanoscale sizeautomatic information storage and nonvolatile characteristicwith respect to long periods of power-down In recent yearsmore and more researchers pay attention to memristive neu-ral networks A novel chaotic neural network withmemristorwas built and applied to associative memory [8] Long-termpotentiation and long-term depression of synapses usingmemristor were realized [9] Memristors as main modulesof complex bionic information processing networks wereutilized [10] and then memristive neural networks weregradually introduced to build memristive cellular automataand discrete-time memristive cellular neural networks [11]

The PID controller based onmemristive CMAC network wasbuilt [12] In addition memristive crossbar arrays are used torealize pulse neural networks [13] andmemristor is utilized tobuild synapse template of cellular neural networks [14]Theseresearch results show that memristor devices are capableof emulating the biological synapses through building upthe correspondence between memristive conductance andsynapse weight Memristor is an ideal choice of electricsynapse of new neuromorphic system In this paper a newperceptron is built to realize combinational logic classifica-tion problems The effectiveness of the memristive percep-tron for combinational logic classification is demonstratedthrough MATLAB simulations

2 Memristive Perceptron

From 2008 the memristor was under development byHewlett-Packard team [15]The change curve of I-V of mem-ristor under sine-type input voltage (V(119905) = plusmn15 sin2(2120587119905))can be seen in Figure 1

The memristive conductance change dgdt is a functionof voltage v in the voltage-controlled memristor [16] Thefunction is similar to sinh curve and the correspondencebetweenmemristive conductance and synapse weight updateis set as

119889119892

119889119905= 120572 sinh (120573V) (1)

2 Mathematical Problems in Engineering

2

1

0

minus1

minus2

119881

0

0

1 2 3119905

times10minus4

119868

05

1

minus05

minus1

(a) V(119905) = plusmn15 sin2(2120587119905)

times10minus5

8

6

4

2

0

minus2

minus4

minus6

minus8minus2 minus1 0 1 2

119881

119868

(b) I-V hysteresis corresponding to the excitation (a)

Figure 1 Characteristic I-V curve of memristor under sine-type input voltage

119889119892119889119905

Figure 2The relationship curve of memristive conductance changeand voltage

1198841

1198842

119884119896

1198831

1198832

1198833

119908119869119868

1

1

11

1

1

sum

sum

sum

sum

sum

sum

119891(middot)

119891(middot)

119891(middot)119891(middot)

119891(middot)

119891(middot)11990811

11988811

119888119896119869

minus1205791

minus1205792

minus120579119869 minus120579998400119896

minus1205799984002

minus1205799984001

119883119868

Figure 3 Memristive perceptron model

where the values of 120572 and 120573 depend on the kind ofmemristorsuch as material size and manufacturing process The rela-tionship curve between the memristive conductance changeand the voltage is shown in Figure 2 It can be seen thatmemristive conductance change dgdt increases along withthe increasing of applied voltage v If the learning error e ofperceptronis regarded as voltage v memristive conductancechange can correspondingly describe as synapse weight Thecorrespondence between memristive conductance changeand synapse weight update can be built

The memristor model is used as synapse of perceptron tobuildmemristive perceptronmodel shown in Figure 3 whosemathematical description is as follows

119884119896= 119891(

119869

sum119895=1

119888119896119895119891(

119868

sum119894=1

119908119895119894119883119894minus 120579119895) minus 120579

1015840

119896) (2)

where 119883119894is the input of neuron 119894 119884

119896is output of neuron 119896

119894 119895 119896 are the numbers of the input layer neurons the hiddenlayer neurons and the output layer neurons respectively 119908

119895119894

represents the memristive synapse weights from the inputlayer neuron 119894 to the hidden layer neuron 119895 119888

119896119895represents

thememristive synapseweights from the hidden layer neuron119895 to the output layer neuron 119896 respectively 120579

119895and 1205791015840

119896

are thresholds of the hidden layer neuron 119895 and outputlayer neuron 119896 respectively 119891 is the step function whosemathematical expression is

119891 (119883) = 0 119883 lt 0

1 119883 ge 0(3)

Mathematical Problems in Engineering 3

119884

1198831

1198832

(a) NAND

1198841198831

1198832

(b) NOR

1198841198831

1198832

(c) XOR

119884

1198831

1198832

(d) NXOR

Figure 4 Graphic symbols of combinational logic

0 05 1 15 2

0

05

1

15

2

1198831

1198832

minus05

minus05minus1

minus1

(a) The classification result of NAND

0 1 2

0

05

1

15

2

1198832

minus05

minus1minus1

1198831

(b) The classification result of NOR

Figure 5 The classification results of NAND and NOR

3 Weight Update Rule of Memristive Synapses

If memristive perceptron is applied to combinational logicclassification weight update rule should be set In expression(1) when Δ119905 is very small dg can be replaced by Δ119892

Δ119892 = 120572 sinh (120573V) times Δ119905 (4)

Let the memristive conductance 119892 correspond to synapseweight 119908 of perceptron and combine BP learning ruleswhich are used as the prototypeThenmemristive perceptronweight-update rule by following the rule through a givenmonitoring signal can be set

Δ119908 (119896) = 120578 sdot 120572 sinh [120573 (119878 (119896) minus 119884 (119896))] sdot 119883

119908 (119896 + 1) = 119908 (119896) + Δ119908 (119896) (5)

where 120578 = Δ119905 is learning rate 119878(119896) is monitoring signal119884(119896) is output of memristive perceptron 119878(119896) minus 119884(119896) is errorof memristive perceptron and 119883 is input of memristiveperceptron let 120572 = 4 120573 = 3

4 Memristive Perceptron ImplementsCombinational Logic Classification

The combinational logic operators include the NAND NORXOR and NXOR operations Their graphic symbols areshown in Figure 4 and the corresponding truth table is shownin Table 1

Table 1 Truth table of the combinational logic operators

Input Output119884

1198831

1198832

NAND NOR XOR NXOR0 0 1 1 0 10 1 1 0 1 01 0 1 0 1 01 1 0 0 0 1

41 Realization of Combinational Logic NANDandNORClas-sification It can be seen from Table 1 that the combinationallogic NAND and NOR classification belongs to the linearseparable problems so they can be realized by a two-inputsingle-layer memristive perceptron model Let the threshold120579 = 08344 and the learning rate 120578 = 002 When thenumber of cycles is set to 30 and the initial weight is set toa random nonzero number the experiment result is shownin Figure 5(a) where ldquordquo denotes the output is logic ldquo1rdquoand ldquo◻rdquo denotes the output is logic ldquo0rdquo The classification oflogic NAND operator is realized efficiently Similarly let thethreshold 120579 = 04121 and the learning rate 120578 = 002 Thenumber of cycles is set to 30 so the classification of logicNOR operator is realized efficiently whose experiment resultis shown in Figure 5(b)

42 Realization of Combinational Logic XOR and NXORClassification It can be seen from Table 1 that the combi-national logic XOR and NXOR classification belongs to the


0

05

1

15

2119883

2

minus05

minus10 05 1 15 2

1198831

minus05minus1

1198841

(a) The classification result of 1198841

0 1 2

0

05

1

15

2

1198832

minus1minus1

1198831

1198842

minus05

(b) The classification result of 1198842XOR output

0 1 2

0

05

1

15

2

minus05

minus1minus1

1198841

1198842

(c) Classification result of logic XOR

NXOR output

0

05

1

15

2

minus1

minus05

0 1 2minus1

1198841

1198842

(d) Classification result of logic NXOR

Figure 6 Classification results of the combinational logic XOR and NXOR with the monitoring signal

linear inseparable problems As the single-layer memristiveperceptron is unable to realize the nonlinear classificationproblems [17] a double-layermemristive perceptronmodel isneeded to realize logic XOR and NXOR classification whichis equivalent to the two paralleling single-layer memristiveperceptrons So it can be used to implement logic XOR andNXOR classification problems

Truth table of XOR and NXOR with the monitoringsignal is shown in Table 2 119884

1is the monitoring signal

of the first perceptron in the hidden layer and 1198842is the

monitoring signal of the second perceptron in the hiddenlayer Let 119884

1= [1 1 0 1] 119884

2= [1 0 1 1] both of them

Table 2 Truth table of XOR and NXOR with monitoring signal

Input Supervisor Output1198831

1198832

1198841

1198842

XOR NXOR0 0 1 1 0 10 1 1 0 1 01 0 0 1 1 01 1 1 1 0 1

are linear separable problems So the memristive perceptronin the hidden layer can be used to realize classification Let


0

05

1

15119883

2

minus05

0 05 1 151198831

minus05


0

05

1

15

1198832

minus05

0 05 1 151198831

minus05


0

0

05

05

1

1

15

15

minus05

minus05

1198841

1198832

1198831

(c) The classification result of 1198841

05

1

15119883

2

1198842

minus05

0

0 05 1 15minus05

1198831

(d) The classification result of 1198842XOR output

0

05

1

15

0 05 1 15minus05

minus05

1198841

1198842

(e) Classification result of logic XOR

NXOR output

0

05

1

15

minus05

1198842

0 05 1 15minus05

1198841

(f) Classification result of logic NXOR

Figure 7 Classification results of combinational logic with test input signals


Table 3 The results of whole combinational logic classification

Combinationallogical operator Initial memristive weight Threshold Learning times Final memristive weight Divider equation

NAND 01705 00994 08344 1 minus06309 minus07020 minus063091198831minus 07020119883

2minus 08344 = 0

NOR 03110 minus06576 04121 1 minus12919 minus14591 minus129191198831minus 14591119883

2minus 04121 = 0

1198841

minus08728 minus01908 05440 2 minus08728 06106 minus087281198831+ 06106119883

2minus 05440 = 0

1198842

minus01033 minus02684 08657 3 06981 minus10698 069811198831minus 10698119883

2minus 08657 = 0

XOR 05379 minus02080 03466 3 minus02635 minus02080 minus026351198841minus 02080119884

2minus 03466 = 0

NXOR minus03684 05454 minus07397 3 04330 05454 043301198841+ 05454119884

2+ 07397 = 0

thresholds 1205791= 05440 120579

2= 08657 and learning rate 120578 =

002 and let the number of cycles be 30 the initial weightsare the random nonzero numbersThe experiment results areshown in Figures 6(a) and 6(b) Then 119884

1and 119884

2are looked as

the inputs of memristive perceptron of output layer so 119884 canbe taken as the output In MATLAB program let threshold1205791015840 = 03466 learning rate 120578 = 002 and the number of cyclesbe 30 the experiment result is shown in Figure 6(c) TheXOR classification is realized From the above analysis theprocedure of the logic NXOR is the same as the one of logicXOR Let threshold 1205791015840 = minus07397 learning rate 120578 = 002 andthe number of cycles be 30 the experiment result is shown inFigure 6(d) The NXOR classification is realized

Through the above theoretical analysis and experimentsimulation the results of whole combinational logic classifi-cation are shown in Table 3 It can be seen that NAND andNOR classifications are realized in the single-layer memris-tive perceptron after learning once The XOR and NXORclassifications are realized in the double-layer memristiveperceptron after learning eight times The combinationallogic classification can be realized effectively by the memris-tive perceptron we proposed

5 Test Validity of Memristive Perceptron inCombinational Logic Classification

The experiments have confirmed that the memristive per-ceptrons can achieve the standard combinational logic clas-sification However in fact the standard inputs cannot beobtained so the test signals with the error are introduced totest the validity of memristive perceptrons in combinationallogic classification

Let the test input signals be as follows1198831= [minus0122 0128

1135 0998 0102 0125 1023 0962 0 015 102 108] 1198832

= [minus0181 1028 0126 0988 minus0021 1132 0036 1168 01111021 0041 1068] the memristive perceptrons in Part 4 aretested By MATLAB simulations the classification results areshown in Figure 7

It can be known from the above experiments that whenthe test signals with the error are used as inputs the memris-tive perceptrons also can effectively realize the combinationallogic classification

6 Conclusions

The relationship between the synaptic weight update inperceptron and memristive conductance change is linked bythe theoretical deduction A new synaptic weight update ruleis proposed in this paper Single-layer memristive perceptronis proposed to realize the classification of the linear separablelogic NAND and NOR Double-layer memristive perceptronis built to realize the classification of linear inseparable logicXOR and NXOR The experiments exhibit that memristiveperceptron can effectively implement the combinational logicclassification The memristive perceptron has simple struc-ture and high integration so that it is easier to be implementedby the low-power circuit The more complex memristiveneural networks we used the more complex problems can besolved in artificial intelligence field

Acknowledgments

The work was supported by the National Natural ScienceFoundation of China (Grant nos 60972155 61101233) Fun-damental Research Funds for the Central Universities (Grantnos XDJK2012A007 XDJK2013B011) University ExcellentTalents Supporting Foundations in of Chongqing (Grant no2011-65) University Key Teacher Supporting Foundations ofChongqing (Grant no 2011-65) Technology Foundation forSelected Overseas Chinese Scholars Ministry of Personnel inChina (Grant no 2012-186) Spring Sunshine Plan ResearchProject of the Ministry of Education of China (Grant noz2011148)

References

[1] M-YHePrinciples Language Design andApplication ofNeuralComputing Press of Xidian University Xian China 1992

[2] Y Zhang J Wang and Y Xia ldquoA dual neural network forredundancy resolution of kinematically redundant manipu-lators subject to joint limits and joint velocity limitsrdquo IEEETransactions on Neural Networks vol 14 no 3 pp 658ndash6672003

[3] A Datta and B Biswas ldquoA fuzzy multilayer perceptron net-work based detection and classification of lobar intra-cerebralhemorrhage from computed tomography images of brainrdquo inProceedings of the International Conference on Recent Trends inInformation Systems pp 257ndash262 2011


[4] A Gkanogiannis and T Kalamboukis ldquoA perceptron-like linearsupervised algorithm for text classificationrdquo in Advanced DataMining and Applications vol 6440 of Lecture Notes in ComputerScience pp 86ndash97 2010

[5] Y C Hu ldquoPattern classification by multi-layer perceptronusing fuzzy integral-based activation functionrdquo Applied SoftComputing Journal vol 10 no 3 pp 813ndash819 2010

[6] M Fernandez-Delgado J Ribeiro E Cernadas and S BarroldquoFast weight calculation for kernel-based perceptron in two-class classification problemsrdquo in Proceedings of the InternationalJoint Conference on Neural Networks (IJCNN rsquo10) pp 1ndash6 July2010

[7] I EI-Feghi A Tahar andM Ahmadi ldquoEfficient features extrac-tion for fingerprint classification with multi layer perceptronneural networkrdquo in Proceedings of International Symposium onSignals Circuits and Systems pp 1ndash4 2011

[8] X-F Hu S-K Duan and L-D Wang ldquoA novel chaotic neuralnetwork using memristors with applications in associativememoryrdquo Abstract and Applied Analysis vol 2012 Article ID405739 19 pages 2012

[9] S Choi and G Kim ldquoSynaptic behaviors and modelling of ametal oxide memristive devicerdquo Applied Physics A MaterialsScience amp Processing vol 102 no 4 pp 1019ndash1025 2011

[10] A Mittal and S Swaminathan ldquoEmulating reflex actionsthrough memristorsrdquo in Proceedings of IEEE Conference andExhibition (GCC rsquo11) pp 469ndash472 2011

[11] M Itoh and L O Chua ldquoMemristor cellular automata andmemristor discrete-time cellular neural networksrdquo Interna-tional Journal of Bifurcation and Chaos vol 19 no 11 pp 3605ndash3656 2009

[12] L-DWang X-Y Fang S-K Duan et al ldquoPID controller basedon memristive CMAC networkrdquo Abstract and Applied Analysisvol 2013 Article ID 510238 6 pages 2013

[13] A Afifi A Ayatollahi and F Raissi ldquoImplementation ofbiologically plausible spiking neural network models on thememristor crossbar-based CMOSnano circuitsrdquo in Proceedingsof EuropeanConference onCircuitTheory andDesignConferenceProgram (ECCTD rsquo09) pp 563ndash566 August 2009

[14] S-Y Gao S-K Duan and L-DWang ldquoOnmemristive cellularneural network and its applications in noise removal and edgeextractionrdquo Journal of Southwest University vol 33 no 11 pp63ndash70 2011

[15] D B Strukov G S Snider D R Stewart and R S WilliamsldquoThe missing memristor foundrdquo Nature vol 453 no 7191 pp80ndash83 2008

[16] A Afifi A Ayatollahi and F Raissi ldquoSTDP implementationusing memristive nanodevice in CMOS-Nano neuromorphicnetworksrdquo IEICE Electronics Express vol 6 no 3 pp 148ndash1532009

[17] J-G Yang Artificial Neural Network Practical Guide Press ofZhejiang University Hangzhou China 2001

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


2

1

0

minus1

minus2

119881

0

0

1 2 3119905

times10minus4

119868

05

1

minus05

minus1

(a) V(119905) = plusmn15 sin2(2120587119905)

times10minus5

8

6

4

2

0

minus2

minus4

minus6

minus8minus2 minus1 0 1 2

119881

119868

(b) I-V hysteresis corresponding to the excitation (a)

Figure 1 Characteristic I-V curve of memristor under sine-type input voltage

119889119892119889119905

Figure 2The relationship curve of memristive conductance changeand voltage

1198841

1198842

119884119896

1198831

1198832

1198833

119908119869119868

1

1

11

1

1

sum

sum

sum

sum

sum

sum

119891(middot)

119891(middot)

119891(middot)119891(middot)

119891(middot)

119891(middot)11990811

11988811

119888119896119869

minus1205791

minus1205792

minus120579119869 minus120579998400119896

minus1205799984002

minus1205799984001

119883119868

Figure 3 Memristive perceptron model

where the values of 120572 and 120573 depend on the kind ofmemristorsuch as material size and manufacturing process The rela-tionship curve between the memristive conductance changeand the voltage is shown in Figure 2 It can be seen thatmemristive conductance change dgdt increases along withthe increasing of applied voltage v If the learning error e ofperceptronis regarded as voltage v memristive conductancechange can correspondingly describe as synapse weight Thecorrespondence between memristive conductance changeand synapse weight update can be built

The memristor model is used as synapse of perceptron tobuildmemristive perceptronmodel shown in Figure 3 whosemathematical description is as follows

119884119896= 119891(

119869

sum119895=1

119888119896119895119891(

119868

sum119894=1

119908119895119894119883119894minus 120579119895) minus 120579

1015840

119896) (2)

where 119883119894is the input of neuron 119894 119884

119896is output of neuron 119896

119894 119895 119896 are the numbers of the input layer neurons the hiddenlayer neurons and the output layer neurons respectively 119908

119895119894

represents the memristive synapse weights from the inputlayer neuron 119894 to the hidden layer neuron 119895 119888

119896119895represents

thememristive synapseweights from the hidden layer neuron119895 to the output layer neuron 119896 respectively 120579

119895and 1205791015840

119896

are thresholds of the hidden layer neuron 119895 and outputlayer neuron 119896 respectively 119891 is the step function whosemathematical expression is

119891 (119883) = 0 119883 lt 0

1 119883 ge 0(3)


119884

1198831

1198832

(a) NAND

1198841198831

1198832

(b) NOR

1198841198831

1198832

(c) XOR

119884

1198831

1198832

(d) NXOR


0 05 1 15 2

0

05

1

15

2

1198831

1198832

minus05

minus05minus1

minus1


0 1 2

0

05

1

15

2

1198832

minus05

minus1minus1

1198831





Δ119892 = 120572 sinh (120573V) times Δ119905 (4)



119908 (119896 + 1) = 119908 (119896) + Δ119908 (119896) (5)





Input Output119884

1198831

1198832

NAND NOR XOR NXOR0 0 1 1 0 10 1 1 0 1 01 0 1 0 1 01 1 0 0 0 1




0

05

1

15

2119883

2

minus05

minus10 05 1 15 2

1198831

minus05minus1

1198841


0 1 2

0

05

1

15

2

1198832

minus1minus1

1198831

1198842

minus05


0 1 2

0

05

1

15

2

minus05

minus1minus1

1198841

1198842


NXOR output

0

05

1

15

2

minus1

minus05

0 1 2minus1

1198841

1198842








1= [1 1 0 1] 119884




1198832

1198841

1198842

XOR NXOR0 0 1 1 0 10 1 1 0 1 01 0 0 1 1 01 1 1 1 0 1



0

05

1

15119883

2

minus05

0 05 1 151198831

minus05


0

05

1

15

1198832

minus05

0 05 1 151198831

minus05


0

0

05

05

1

1

15

15

minus05

minus05

1198841

1198832

1198831


05

1

15119883

2

1198842

minus05

0

0 05 1 15minus05

1198831


0

05

1

15

0 05 1 15minus05

minus05

1198841

1198842


NXOR output

0

05

1

15

minus05

1198842

0 05 1 15minus05

1198841







2minus 08344 = 0


2minus 04121 = 0

1198841


2minus 05440 = 0

1198842


2minus 08657 = 0


2minus 03466 = 0

NXOR minus03684 05454 minus07397 3 04330 05454 043301198841+ 05454119884

2+ 07397 = 0

thresholds 1205791= 05440 120579



1and 119884

2are looked as






1135 0998 0102 0125 1023 0962 0 015 102 108] 1198832



6 Conclusions


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










119884

1198831

1198832

(a) NAND

1198841198831

1198832

(b) NOR

1198841198831

1198832

(c) XOR

119884

1198831

1198832

(d) NXOR


0 05 1 15 2

0

05

1

15

2

1198831

1198832

minus05

minus05minus1

minus1


0 1 2

0

05

1

15

2

1198832

minus05

minus1minus1

1198831





Δ119892 = 120572 sinh (120573V) times Δ119905 (4)



119908 (119896 + 1) = 119908 (119896) + Δ119908 (119896) (5)





Input Output119884

1198831

1198832

NAND NOR XOR NXOR0 0 1 1 0 10 1 1 0 1 01 0 1 0 1 01 1 0 0 0 1




0

05

1

15

2119883

2

minus05

minus10 05 1 15 2

1198831

minus05minus1

1198841


0 1 2

0

05

1

15

2

1198832

minus1minus1

1198831

1198842

minus05


0 1 2

0

05

1

15

2

minus05

minus1minus1

1198841

1198842


NXOR output

0

05

1

15

2

minus1

minus05

0 1 2minus1

1198841

1198842








1= [1 1 0 1] 119884




1198832

1198841

1198842

XOR NXOR0 0 1 1 0 10 1 1 0 1 01 0 0 1 1 01 1 1 1 0 1



0

05

1

15119883

2

minus05

0 05 1 151198831

minus05


0

05

1

15

1198832

minus05

0 05 1 151198831

minus05


0

0

05

05

1

1

15

15

minus05

minus05

1198841

1198832

1198831


05

1

15119883

2

1198842

minus05

0

0 05 1 15minus05

1198831


0

05

1

15

0 05 1 15minus05

minus05

1198841

1198842


NXOR output

0

05

1

15

minus05

1198842

0 05 1 15minus05

1198841







2minus 08344 = 0


2minus 04121 = 0

1198841


2minus 05440 = 0

1198842


2minus 08657 = 0


2minus 03466 = 0

NXOR minus03684 05454 minus07397 3 04330 05454 043301198841+ 05454119884

2+ 07397 = 0

thresholds 1205791= 05440 120579



1and 119884

2are looked as






1135 0998 0102 0125 1023 0962 0 015 102 108] 1198832



6 Conclusions


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

05

1

15

2119883

2

minus05

minus10 05 1 15 2

1198831

minus05minus1

1198841


0 1 2

0

05

1

15

2

1198832

minus1minus1

1198831

1198842

minus05


0 1 2

0

05

1

15

2

minus05

minus1minus1

1198841

1198842


NXOR output

0

05

1

15

2

minus1

minus05

0 1 2minus1

1198841

1198842








1= [1 1 0 1] 119884




1198832

1198841

1198842

XOR NXOR0 0 1 1 0 10 1 1 0 1 01 0 0 1 1 01 1 1 1 0 1



0

05

1

15119883

2

minus05

0 05 1 151198831

minus05


0

05

1

15

1198832

minus05

0 05 1 151198831

minus05


0

0

05

05

1

1

15

15

minus05

minus05

1198841

1198832

1198831


05

1

15119883

2

1198842

minus05

0

0 05 1 15minus05

1198831


0

05

1

15

0 05 1 15minus05

minus05

1198841

1198842


NXOR output

0

05

1

15

minus05

1198842

0 05 1 15minus05

1198841







2minus 08344 = 0


2minus 04121 = 0

1198841


2minus 05440 = 0

1198842


2minus 08657 = 0


2minus 03466 = 0

NXOR minus03684 05454 minus07397 3 04330 05454 043301198841+ 05454119884

2+ 07397 = 0

thresholds 1205791= 05440 120579



1and 119884

2are looked as






1135 0998 0102 0125 1023 0962 0 015 102 108] 1198832



6 Conclusions


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

05

1

15119883

2

minus05

0 05 1 151198831

minus05


0

05

1

15

1198832

minus05

0 05 1 151198831

minus05


0

0

05

05

1

1

15

15

minus05

minus05

1198841

1198832

1198831


05

1

15119883

2

1198842

minus05

0

0 05 1 15minus05

1198831


0

05

1

15

0 05 1 15minus05

minus05

1198841

1198842


NXOR output

0

05

1

15

minus05

1198842

0 05 1 15minus05

1198841







2minus 08344 = 0


2minus 04121 = 0

1198841


2minus 05440 = 0

1198842


2minus 08657 = 0


2minus 03466 = 0

NXOR minus03684 05454 minus07397 3 04330 05454 043301198841+ 05454119884

2+ 07397 = 0

thresholds 1205791= 05440 120579



1and 119884

2are looked as






1135 0998 0102 0125 1023 0962 0 015 102 108] 1198832



6 Conclusions


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













2minus 08344 = 0


2minus 04121 = 0

1198841


2minus 05440 = 0

1198842


2minus 08657 = 0


2minus 03466 = 0

NXOR minus03684 05454 minus07397 3 04330 05454 043301198841+ 05454119884

2+ 07397 = 0

thresholds 1205791= 05440 120579



1and 119884

2are looked as






1135 0998 0102 0125 1023 0962 0 015 102 108] 1198832



6 Conclusions


Acknowledgments


References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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Research Article Memristive Perceptron for Combinational