XOR Logic Functions Research Articles

Design and Simulation of a Multilayer Chemical Neural Network That Learns via Backpropagation.

The design and implementation of adaptive chemical reaction networks, capable of adjusting their behavior over time in response to experience, is a key goal for the fields of molecular computing and DNA nanotechnology. Mainstream machine learning research offers powerful tools for implementing learning behavior that could one day be realized in a wet chemistry system. Here we develop an abstract chemical reaction network model that implements the backpropagation learning algorithm for a feedforward neural network whose nodes employ the nonlinear "leaky rectified linear unit" transfer function. Our network directly implements the mathematics behind this well-studied learning algorithm, and we demonstrate its capabilities by training the system to learn a linearly inseparable decision surface, specifically, the XOR logic function. We show that this simulation quantitatively follows the definition of the underlying algorithm. To implement this system, we also report ProBioSim, a simulator that enables arbitrary training protocols for simulated chemical reaction networks to be straightforwardly defined using constructs from the host programming language. This work thus provides new insight into the capabilities of learning chemical reaction networks and also develops new computational tools to simulate their behavior, which could be applied in the design and implementations of adaptive artificial life.

Improving the performance of all-optical logic gates based on metal-insulator-metal heterogeneous plasmonic waveguide by Kerr nonlinearity effect

In this paper, the nonlinear effect of Kerr on increasing the efficiency of multi-channel all-optical metal-insulator-metal logic gates with heterogeneous metals is investigated. In this study, linear interference between surface plasmonic polariton modes has been employed. The performance of OR, AND, XOR and NOR gates is numerically analyzed by the finite element method. A structure with fixed physical dimensions can manage several basic logic functions. By applying optical signals to various input ports in the proposed structure, we can implement OR, AND, and XOR logic functions. The NOR logic gate can be established by the addition of a control optical signal. It has been shown that the nonlinear material of Kerr increases the difference of field intensity between logic levels of "0" and "1" that are 77 V/m for OR gate, 133 V/m for AND gate, 89 V/m for XOR gate, and 138 V/m for NOR gate. Also, simulation results show the minimum extinction ratio (ER) of 33.5, 36.4, 45.4, and 42.4 dB for OR, AND, XOR, and NOR logic gates, respectively. The proposed all-optical logic gate has a simple and compact arrangement and it can be applied to many nanophotonic components used in optical communication networks.

Temperature response of all-optical XOR logic function based on different semiconductor optical amplifiers

A critical area of research is studying the performance of semiconductor optical amplifiers (SOAs) at high temperatures. In this paper, the performance of all-optical exclusive-OR (XOR) logic gate is investigated at high operating temperatures (TOP) using different SOAs technologies such as conventional SOAs, carrier reservoir (CR)-SOAs, reflective SOAs (RSOAs), and photonic crystal (PC)-SOAs, for the first time to our knowledge. The time-dependent differential equations of SOAs, CR-SOA, RSOAs, and PC-SOAs at different operating data rates have been solved. The performance of the XOR logic gate is evaluated by calculating the quality factors and plotting the eye diagrams for each amplifier. Besides, the dependence of the key operating parameters on the TOP is examined and assessed for each scheme. The results showed that the RSOAs perform better at high temperatures than other proposed SOA technologies.

A Single Transistor‐Based Threshold Switch for a Bio‐Inspired Reconfigurable Threshold Logic

AbstractIn this work, a single transistor‐based threshold switch for a bio‐inspired reconfigurable threshold logic is demonstrated with a metal‐oxide‐semiconductor field‐effect transistor. A threshold logic can mimic biological neurons of brain by use of Boolean entities with threshold units. Various linear Boolean logic functions of AND, OR, NOT, NAND, and NOR are implemented without analog circuits such as a comparator for threshold operation. As a result, reconfigurable threshold logic is realized with a 6F2 footprint. In addition to linearly separable logic functions, a linearly inseparable XOR logic function is also implemented using the same threshold switch. Edge detection, which is one of the most important functions for image recognition, is also demonstrated using the XOR logic function with the aid of semi‐empirical circuit simulation by reflecting experimental data.

Cryptographic Key Generation and In Situ Encryption in One‐Transistor‐One‐Resistor Memristors for Hardware Security

AbstractThe problem of hardware security is exacerbating in the artificial intelligence & Internet of Things era. Physical unclonable function (PUF) is a promising security primitive that exploits the intrinsic random variations in electronic hardware to produce digital keys. Here, it is shown for the first time that the subthreshold slope (S.S) variations of the transistors can be utilized as the entropy source of the PUF to generate the physical keys. By combining this S.S PUF with a memristor‐based XOR logic function, an in situ encryption/decryption scheme is proposed in a compact one‐transistor‐one‐resistor (1T1R) architecture. It is experimentally demonstrated that the S.S PUF shows great reproducibility, uniqueness, and uniformity. Using the S.S PUF keys, encryption and decryption are successfully implemented for three 16‐bit binary sequences in 1T1R devices. The results demonstrate that the unique features of 1T1R can enlighten functional design at the device level against hardware security threats, and the security, memory, and computing can be realized on the same device.

A reconfigurable scheme for realization of electro-optical logic gate based on silicon-graphene Mach–Zhender interferometer

In this paper, we propose a reconfigurable scheme for implementation of an electro-optical logic gate by utilizing a Mach–Zehnder interferometer (MZI)-based structure. In order to achieve high performance and small footprint for the proposed logic gate, we have used a compact, broadband, low power and high speed MZI-based electro-optical switch which consists of a silicon-graphene slot waveguide as phase shifter in each arm of the MZI structure. Our design can perform electro-optical AND, OR and XOR logic functions in three different operational modes by using three electrical control signals. The functionality of the reconfigurable electro-optical logic gate is investigated with the help of eye diagram analysis for all three operational modes. Simulation results show that the proposed reconfigurable logic gate is able to work under at least 62.5 Gbit/s with high extinction ratio (ER) about 24.6 dB for transverse electric polarization mode at telecommunication wavelength of 1.55 [Formula: see text]m.

Ultra-compact all-optical phase-controlled NAND, OR, XOR, XNOR, and NOT multi-function logic gate

We propose a novel multi-function logic gate in order to attain all NAND, OR, XOR, XNOR, and NOT logic functions in a single structure with controlling the phase of input lights. Beam propagation analysis illustrates that the highest insertion loss of structure is − 0.05 dB in whole C-band. The output on–off logic level contrast ratio for NAND, OR, XOR, XNOR, and NOT logic functions are 28.2, 28.2, 30.2, 30.2, and 30.2 dB, respectively. The structure which is composed of one multimode interference region with ultra-small size of 1.5 µm × 12.2 µm is a promising candidate for ultra-compact systems.

Implementation of 1×2 decoder and XOR-XNOR logic functions on a PhC structure

In this article, a photonic crystal based 1 × 2 decoder is proposed with dual output logic using T-shaped beam splitters and waveguides which can also be used for the concurrent implementation of XOR and XNOR logic functions. The type of interference at two T-shaped junctions is determined by the phase difference of the input light beams. Phase of the light defines the input logic whereas the light intensity discriminates the output. The proposed design has resulted with a high contrast ratio of 41.9 dB and 29.4 dB at a bit rate of 2.10 Tbps and 1.29 Tbps, at the output ports Y0 and Y1, respectively. Furthermore, the calculated fabrication tolerance of the proposed structure shows that the splitter rod's radius can be allowed to vary within ±5% from the optimal value. This results in a small change of 4.4% and 2.3% from the observed value of the contrast ratio at the ports Y0 and Y1, respectively, which is trivial.

Nonvolatile reconfigurable sequential logic in a HfO2 resistive random access memory array.

Resistive random access memory (RRAM) based reconfigurable logic provides a temporal programmable dimension to realize Boolean logic functions and is regarded as a promising route to build non-von Neumann computing architecture. In this work, a reconfigurable operation method is proposed to perform nonvolatile sequential logic in a HfO2-based RRAM array. Eight kinds of Boolean logic functions can be implemented within the same hardware fabrics. During the logic computing processes, the RRAM devices in an array are flexibly configured in a bipolar or complementary structure. The validity was demonstrated by experimentally implemented NAND and XOR logic functions and a theoretically designed 1-bit full adder. With the trade-off between temporal and spatial computing complexity, our method makes better use of limited computing resources, thus provides an attractive scheme for the construction of logic-in-memory systems.

Thiazolidine based differential chromo-fluorescent sensor for Cu2+ and CN− ions: Elaboration as logic devices

Thiazolidine based probe 1 has been synthesized for selective estimation of Cu2+ ions amongst other metal ions viz., Zn2+, Co2+, Ca2+, K+, Ni2+, Mn2+, Fe2+, Hg2+, Na+, Pb2+, Ba2+, Fe3+, Al3+, Cr3+. The probe 1 has opened new absorption channels at 300nm and 500nm in the presence of Cu2+ ions. The ratiometric response has been observed in the presence of Cu2+ ions due to emission quenching at 425nm and enhancement at 485nm that resulted in “ON–OFF–ON” type sensing. The probe 1 has been used to estimate Cu2+ ions between 50nM and 15µM, which is much lower than recommended by WHO in drinking water (30µM). The probe 1 has also shown selective ratiometric absorption behavior towards CN− ions in CH3CN: H2O: 1:1. The ratiometric behavior of the probe 1 in the presence of Cu2+ and CN− ions has mimicked as XOR logic function at λem 485nm and YES logic gate at λabs 300nm. The sensing mechanisms of the probe 1 toward Cu2+ and CN− ions have been theoretically supported by DFT and TD-DFT calculations. Probe 1 has been used for its practical aplicability to sense Cu2+ and CN− through dip coating method.

Design and Analysis of XOR Logic Gate Based on Two-Photon Absorption

Two-photon absorption with high intensity pump beam occurs in a SOA depends on fast phase change of a weak probe signal. This work analysed optical XOR logic function using two-photon absorption induced fast phase change. A rate equation for SOA and both input data signals A and B with high intensity, configured in the form of MZI has also been proved. The model shows that XOR operation at 10 Gb/s with good signal to noise ratio is obtained with high input intensities. The result on the generation of XOR indicates that operations on 10 Gb/s with a high signal to noise ratio can easily be implemented. The average input power into the SOA is 20 dbm corresponding to the peak power of 5.5 dBm at 10 Gb/s when the width of the input pulse 3.6 ps. The short narrow pulse width is utilised in the study for stronger effect of two-photon absorption.

MMI-Based Simultaneous All-Optical XOR–NAND–OR and XNOR–NOT Multilogic Gate for Phase-Based Signals

We propose a novel design to simultaneously access various optical logic functions from different output ports. Logical values of inputs and outputs are defined in phase and intensity area of light, respectively. The proposed structure is composed of one multimode interference waveguide with the ultrasmall size of 2.5 μm × 21 μm. Three output ports of proposed structure offer XOR, NAND, and OR logic functions. In addition, XNOR and NOT logic gates are realized by considering some changes in the conditions. Beam propagation method has been utilized to accomplish the simulations of light propagation. Simulation results of structure in whole C-band show that the maximum insertion loss is -0.14 dB and the least contrast ratio achieved for XOR, NAND, OR, XNOR, and NOT logic functions are 26, 24.7, 25.9, 26, and 25 dB, respectively.

Investigation of a simultaneous multifunctional photonic logic gate based on bidirectional FWM

We demonstrate a multi-functional photonic logic gate for RZ-PolSK signals based on four wave mixing (FWM) in highly nonlinear fiber (HNLF). Bidirectional operation with one spool of HNLF is implemented numerically at 40Gb/s. The basic logic arithmetics, such as XOR, AB¯,A¯B, XNOR, AND, NOR, and complex logic functions such as half-subtracter, half-adder, comparator and decoder are simultaneously realized by adjusting the polarization controllers. This novel structure is low-cost and rather flexible. Proper logic results, clear waveforms and high Q factors of eye diagrams are presented. Simulation analysis shows that bit error-free operation for the logic gate can be obtained when the wavelength separation is from −7 to 6nm for two input signals. The impact of the input power on the Q factor is also investigated. Due to the femoto-second response time of Kerr-effect in HNLF we used in the scheme, the logic gate has great potential in future ultra-high speed optical transmission systems.

Connectable DNA Logic Gates: OR and XOR Logics

Modern computer processors are based on semiconductor logic gates connected to each other in complex circuits. This study contributes to the development of a new class of connectable logic gates made of DNA in which the transfer of oligonucleotide fragments as input/output signals occurs upon hybridization of DNA sequences. The DNA strands responsible for a logic function form associates containing immobile DNA four-way junction structures when the signal is high and dissociate into separate strands when the signal is low. A basic set of logic gates (NOT, AND, and OR) was designed. Two NOT gates, two AND gates, and an OR gate were connected in a network that corresponds to an XOR logic function. The design of the logic gates presented here may contribute to the development of the first biocompatible molecular computer.

All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire

We demonstrate an all-optical XOR logic function for 40Gb/s differential phase-shift keyed (DPSK) data signals in the C-band, based on four-wave mixing (FWM) in a silicon nanowire. Error-free operation with a system penalty of ~3.0dB and ~4.3dB at 10⁻⁹ BER is achieved.

All-optical logic gates based on two-photon absorption in semiconductor optical amplifiers

When the two-photon absorption of a high intensity pump beam takes place in a semiconductor optical amplifier there is an associated fast phase change of a weak probe signal. A scheme to realize fast all-optical XOR logic function using two-photon absorption induced phase change has been analyzed. Rate equations for semiconductor optical amplifiers, for input data signals with high intensity, configured in the form of a Mach–Zehnder interferometer has been solved. The input intensities are high enough so that the two-photon induced phase change is larger than the regular gain induced phase change. The model shows that both XOR operation and pseudo-random binary sequence generation at 250 Gb/s with good signal to noise ratio is feasible.

Use of periodic and monotonic activation functions in multilayer feedforward neural networks trained by extended Kalman filter algorithm

The authors investigate the convergence and pruning performance of multilayer feedforward neural networks with different types of neuronal activation functions in solving various problems. Three types of activation functions are adopted in the network, namely, the traditional sigmoid function, the sinusoidal function and a periodic function that can be considered as a combination of the first two functions. To speed up the learning, as well as to reduce the network size, the extended Kalman filter (EKF) algorithm conjunct with a pruning method is used to train the network. The corresponding networks are applied to solve five typical problems, namely, 4-point XOR logic function, parity generation, handwritten digit recognition, piecewise linear function approximation and sunspot series prediction. Simulation results show that periodic activation functions perform better than monotonic ones in solving multicluster classification problems. Moreover, the combined periodic activation function is found to possess the fast convergence and multicluster classification capabilities of the sinusoidal activation function while keeping the robustness property of the sigmoid function required in the modelling of unknown systems.

ADAPTIVE TRAINING AND PRUNING FOR NEURAL NETWORKS:ALGORITHMS AND APPLICATION

Finding an optimal network size is one of the major concerns when building a neural network. In using the local extended Kalman filter (EKF) algorithm, we propose an efficient approach that combines EKF training and pruning as a whole. In particular, the covariance matrix obtained along with the local EKF training can be utilized to indicate the importance of the network weights. As a result, the network size can be determined adaptively to keep pace with the changes in input characteristics. The effectiveness of this algorithm is demonstrated on generalized XOR logic function and handwritten digit recognition.

Beam-propagation analysis of tapered nonlinear directional couplers

We analyze symmetric and parallel nonlinear directional couplers with the finite-difference beam-propagation method. The results exhibit a cutoff phenomenon of an antisymmetric mode. We also investigate tapered nonlinear couplers for their possible applications to all-optical logic gates. The numerical results show that tapered nonlinear couplers can provide an XOR (eXclusive OR) logic function. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 15: 43–46, 1997.

Programmable optical logic systems using free-space optical interconnections

A free-space optical logic technique is presented that utilizes a two-dimensional array of diffractive optical elements. Each optical element focuses light to multiple, separate positions in the output focal plane. The focal spots from different optical elements are allowed to overlap spatially, resulting in interference. By changing the phase shift between the optical elements, one can create different optical logic operations in the focal plane. The technique is demonstrated by the use of two input beams incident onto a multiplexed optical element written onto a programmable spatial light modulator. The optical element simultaneously creates both AND and XOR logic functions in the output plane.