Ternary Logic Research Articles

Design of an optical half-adder based on two-dimensional photonic crystals using feedforward neural networks

The optical half-adder is one of the important components in the design of optical digital circuits. In this study, an optical half-adder based on two-dimensional photonic crystals with a square lattice has been designed, optimized, and simulated. A feedforward neural network model is used to achieve the optimal state by selecting the defect rod dimension and phase of the input laser to optimize the performance of the optical device. The results show that the proposed structure has an appropriate power difference in both high and low logic states, which results in fewer errors in detecting logical values at the outputs. Another feature of this structure is the use of a minimal number of defect rods and the absence of ring resonators, which leads to a reduction in size and propagation delay time of light in the structure. Moreover, due to its aforementioned features and small size, this structure is suitable for use in integrated optical circuits.

The algebra of ordinary discourse. On the semantics of Cooper’s logic

Abstract We develop an algebraic study of W.S. Cooper’s three-valued propositional logic of ordinary discourse ( $$\mathcal{O}\mathcal{L}$$ O L ). This logic displays a number of unusual features: $$\mathcal{O}\mathcal{L}$$ O L is not weaker but incomparable with classical logic, it is connexive, paraconsistent and contradictory. As a non-structural logic, $$\mathcal{O}\mathcal{L}$$ O L cannot be algebraized by the standard methods. However, we show that $$\mathcal{O}\mathcal{L}$$ O L has an algebraizable structural companion, and determine its equivalent semantics, which turns out to be a finitely-generated discriminator variety. We provide an equational and a twist presentation for this class of algebras, which allow us to compare it with other well-known algebras of non-classical logics. In this way we establish that $$\mathcal{O}\mathcal{L}$$ O L is definitionally equivalent to an expansion of the three-valued logic $${\mathcal {J}}3$$ J 3 of D’Ottaviano and da Costa, itself a schematic extension of paraconsistent Nelson logic.

Mixed-Dimensional Semiconductors-Based Ternary Circuits with Tunable Negative Transconductance Characteristics.

Multivalued logic (MVL) systems, in which data are processed with more than two logic values, are considered a viable solution for achieving superior processing efficiency with higher data density and less complicated system complexity without further scaling challenges. Such MVL systems have been conceptually realized by using negative transconductance (NTC) devices whose channels consist of van der Waals (vdW) heterojunctions of low-dimensional semiconductors; however, their circuit operations have not been quite ideal for driving multiple stages in real circuit applications due to reasons such as a reduced output swing and poorly defined logic states. Herein, we demonstrate ternary inverter circuits with near rail-to-rail swing and three distinct logic states by employing vdW p-n heterojunctions of single-walled carbon nanotubes (SWCNT) and MoS2 where the SWCNT layer completely covers the MoS2 layer. In particular, SWCNTs are inkjet printed to form heterojunctions with MoS2 grown by chemical vapor deposition (CVD), and both inkjet printing and CVD are fully scalable device fabrication methods for low-dimensional materials. In addition, the NTC characteristics of heterojunction field-effect transistors (H-FETs) are explained based on the electrical characteristics of individual SWCNT and MoS2 channels. By adjustment of the p-channel characteristics in H-FETs by exploiting the advantages of the inkjet printing technology, the widths of the NTC regions are easily adjusted accordingly. The extended NTC region enables stable middle logic state operations of low-dimensional semiconductors-based ternary inverters over a sufficiently wide input voltage range.

Logic-in-memory cell enabling binary and ternary Boolean logics

Logic-in-memory cell enabling binary and ternary Boolean logics

High-performance ternary logic circuits and neural networks based on carbon nanotube source-gating transistors.

Multi-valued logics (MVLs) offer higher information density, reduced circuit and interconnect complexity, lower power dissipation, and faster speed over conventional binary logic system. Recent advancement in MVL research, particularly with emerging low-dimensional materials, suggests that breakthroughs may be imminent if multistates transistors can be fabricated controllably for large-scale integration. Here, a concept of source-gating transistors (SGTs) is developed and realized using carbon nanotubes (CNTs). By extending the source electrode into the channel of conventional CNT transistors, a controllable p-n homojunction is formed, allowing CNT-SGTs to reliably switch between three distinct states. Capitalizing on the straightforward fabrication process of CNT-SGTs, ternary inverters, NMIN and NMAX logic gates, ternary SRAM cells, and a ternary neural network achieving 100% image classification accuracy have been successfully implemented. This study represents the most advanced and highest-performing ternary circuits realized with low-dimensional materials to date. This progress highlights the potential of CNT-SGTs in driving the future of MVL architectures.

Preeminent designing of complementary ternary TRANSFER and COMPLEMENT alongside excitation modulated molecular logic systems.

This article describes an optically adjustable, dual complementary ternary molecular TRANSFER and COMPLEMENT logic gate as well as an extremely rare design of excitation-modulated logic systems using a pyrene coupled bis(indolyl)methane derivative (1) in Brij-58 micelles, triggered by different chemical stimuli. We have looked into the optical response of the probe molecule towards variety of analytes, including OH-, CN-, Hg2+, EDTA etc., at various excitation channels, in order to achieve this goal. By utilizing the probe's intriguingly distinct absorption spectra in response to the injection of OH-, Hg2+, and CN- individually or in succession, tunable molecular ternary logic systems were created. In the current report, fundamental and combinational array structures for the ternary logic circuits have been proposed. Furthermore, based on discernible fluorescence responses of the probe molecule towards unlike analytes at various emission wavelengths, a new type of excitation-modulated logic system has been developed.

Memristive ternary Łukasiewicz logic based on reading-based ratioed resistive states (3R).

The thirst for more efficient computational paradigms has reignited interest in computation in memory (CIM), a burgeoning topic that pivots on the strengths of more versatile logic systems. Surging ahead in this innovative milieu, multi-valued logic systems have been identified as possessing the potential to amplify storage density and computation efficacy. Notably, ternary logic has attracted widespread research owing to its relatively lower computational and storage complexity, offering a promising alternative to the traditional binary logic computation. This study provides insight into the feasibility of ternary logic in the CIM domain using resistive random-access memory (ReRAM) devices. Its multi-level programming capability making it an ideal conduit for the integration of ternary logic. We focus on ternary Łukasiewicz logic because its computational characteristics are highly suitable for mapping logic values with input and output signals. This approach is characterized by voltage-reading-based output for ease of subsequent utilization and computation and validated in 1T1R crossbar arrays in an integrated ReRAM chip (Memory Advanced Demonstrator 200 mm). In addition, the effect of variability of memristive devices on logical computation and the potential for parallel operation are also investigated.This article is part of the theme issue 'Emerging technologies for future secure computing platforms'.

Self-defined dual charge percolation networks for solution-processed multithreshold transistors

This study demonstrates multithreshold engineering of a solution-processed heterojunction electrochemical transistor using a blend of n-type CdSe tetrapod-shaped nanocrystals (TpNCs) and an n-type polymeric organic semiconductor (OSC). The unique geometry of TpNCs enables a broad concentration range of charge percolation, where charge transfer between TpNC and OSC domains determines multiple threshold voltages. The OSC domain’s threshold voltage shifts from 1 to −1 V as TpNC content increases, while the TpNC domain maintains a threshold above 1.5 V. This allows for stable intermediate states, crucial for multivalued logic operations. Charge percolation and photoluminescence studies show selective charge redistribution, shifting the threshold voltages in the polymer networks. Ternary logic gates, including TNOT, TNAND, and TNOR, based on these heterojunction transistors, were also demonstrated, highlighting the potential of this approach for advanced logic applications.

Interfacial Electronic Charge Trapping and Photonic Carrier Excitation Coupling in Solution-Processed Zinc-Tin Oxide Thin-Film Transistors Applied for Logic Gate Design and Quantized Neural Network.

Components needed in Artificial Intelligence with a higher information capacity are critically needed and have garnered significant attention at the forefront of information technology. This study utilizes solution-processed zinc-tin oxide (ZTO) thin-film phototransistors and modulates the values of VG, which allows for the regulation of electron trapping/detrapping at the ZTO/SiO2 interface. By coupling the excited photonic carrier and electronic trapping, logic gates such as "AND," "OR," "NAND," and "NOR" can be achieved. With the exponential growth in data generation, efficient processing and storage solutions are imperative. However, extensive data transfer between computing units and storage limits the level of artificial neural networks (ANNs). Consequently, quantized neural networks (QNNs) have gained interest for their reduced computational resource requirements and lower consumption. In this context, we introduce an optimized ternary logic circuit based on ZTO devices. By utilizing optical modulation to adjust the turn-on voltage of the single device, we demonstrate the achievement of ternary current states, thereby providing three distinct discrete states. This configuration can be extended to QNN computing, demonstrating multilevel quantized current values for in-memory computation. We achieved a handwriting digit recognition rate of 91.6%, thereby demonstrating reliable QNN hardware performance. This robust QNN performance indicates that the metal oxide phototransistor shows significant potential for future ternary computing systems.

Electron-Beam-Induced Negative Differential Transconductance Homojunction Device Based on van der Waals Materials for Functionally Complete Ternary Computing.

Negative differential transconductance (NDT) devices have emerged as promising candidates for multivalued logic computing, and particularly for ternary logic systems. To enable computation of any ternary operation, it is essential to have a functionally complete set of ternary logic gates, which remains unrealized with current NDT technologies, posing a critical limitation for higher-level circuit design. Additionally, NDT devices typically rely on heterojunctions, complicating fabrication and impacting reliability due to the introduction of additional materials and interfaces. Here, we utilize an electron beam to develop tungsten diselenide (WSe2) homojunction NDT devices with W-shaped current-voltage (I-V) characteristics. We demonstrate that electron beam enables the manipulation of Se atoms in WSe2, facilitating controllable and spatially precise tailoring of the WSe2 work function. The electron-beam treatment applied to a part of the WSe2 channel induces a lateral homojunction and ultimately results in the W-shaped I-V curves, which enable both one-input and two-input ternary logic gates. We propose and implement a balanced circuit design for two-input ternary NAND, AND, NOR, and OR gates, featuring a low device count, full-swing operation, and minimized output signal variations. Together with three types of ternary inverters also designed in this work, they form a functionally complete set of ternary logic gates─a prerequisite for practical ternary computing. This work addresses a critical gap in the development of NDT-based ternary computing by ensuring functional completeness and highlights the versatility of electron-beam treatment as an engineering tool for tailoring the properties of two-dimensional van der Waals materials.

Ternary Logic Transistors Using Multi-Stacked 2D Electron Gas Channels in Ultrathin Oxide Heterostructures.

2D electron gas field-effect transistors (2DEG-FETs), employing 2DEG formed at an interface of ultrathin (≈6nm) Al2O3/ZnO heterostructure as the active channel, exhibit outstanding drive current (≈215µA), subthreshold swing (≈132mV dec-1), and field effect mobility (≈49.6 cm2V-1 s-1) with a high on/off current ratio of ≈107. It is demonstrated that the Al2O3 upper layer in Al2O3/ZnO heterostructure acts as the source/drain resistance component during transistor operations, and the applied potential to the 2DEG channel is successfully modulated by Al2O3 thickness variations so that the threshold voltage (Vth) is effectively tuned. Remarkably, double-stacked 2DEG-FETs consisting of two Al2O3/ZnO heterostructured 2DEG channels with a single gate exhibit multiple Vth, enabling a ternary logic state in a single device. By inducing a voltage difference between the stacked channels, a sequential operation of the upper and lower FETs is achieved, successfully realizing a stable ternary logic operation.

Digital‐Analog Integrated Optoelectronic Memristor Based on Carbon Dot for Ternary Opto‐Electronic Logic and Sen‐Memory Applications

AbstractOptoelectronic memristor with light as an additional stimulus is generating interest in various remarkable optical‐electrical‐coupled applications. Herein, an optoelectronic memristor with hybrid digital‐analog switching behavior is developed by incorporating carbon dots (CDs) into the polymethylmethacrylate and the polystyrene layers as charge trapping medium. The memristor exhibits tri‐stable digital switching behavior under electro‐optical programming and analog switching behavior under optical programming. For the digital switching, the SET and RESET voltage of the memristor can be modulated through UV light illumination. Taking advantage of the cooperation of electrical and light stimuli, new ternary optoelectronic logic algorithm implementations with all‐electric or all‐optical signals as inputs are proposed. For the analog switching, the device resistance can be gradually modulated through UV light illumination and output intensity‐ and duration‐dependent characteristics. These features endow the memristor with fused image sensing‐and‐memory (sen‐memory) capability without an auxiliary bias. In addition, the sen‐memory can perform image contrast enhancement operation as the preprocessing operation of the human retina, which can improve the subsequent image recognition rate in the processing tasks. The multifunctional memristor highlights the potential for ternary optoelectronic computing and artificial vision applications, and also, is expected to expand the application scopes of CDs.

An efficient design methodology for a tri-state multiplier circuit in carbon nanotube technology

Abstract This study delves into the computational aspects of ternary logic and the use of carbon nanotube field-effect transistors (CNTFETs) to develop an energy-efficient and robust ternary multiplier (TMUL). Leveraging the exceptional qualities of CNTFETs, such as balanced electron and hole mobility and easy modulation of threshold voltage, the research aims to achieve the desired designs. An innovative design method is employed, recommending a reduced count of logic gates for achieving necessary logic levels. These gates are then utilized to manage the activation and deactivation of the primary transistors within the TMUL cell to convey the intended logics to the outputs. Moreover, the suggested design is focused on a single-V DD , enhancing compatibility with the goals of a multi-valued logic platform. The proposed circuit is validated using Synopsis HSPICE simulator and Stanford’s standard 32-nm CNTFET model file. Comparative analysis with existing TMUL designs demonstrates a 25.43% decrease in average power consumption, a 42.24% reduction in power-delay product (PDP), and a 24.69% decrease in energy-delay product (EDP). The design undergoes thorough simulations under various conditions including load variations and process, voltage, and temperature (PVT) fluctuations to confirm its reliability and robustness.

Application of independent computing nodes with three-valued logic for intermachine interaction of heterogeneous industrial automation devices in a single digital production ecosystem

Application of independent computing nodes with three-valued logic for intermachine interaction of heterogeneous industrial automation devices in a single digital production ecosystem

Wittgenstein Versus Hume: The IS-OUGHT Problem – Finally Solved

Abstract This paper shows that Wittgenstein’s situational approach applied to Hume’s is-ought problem leads to the conclusion that this famous Hume thesis is false both in its original version (lack of logical value of deontic sentences) and in its modern understanding (logical separation of deontic sentences and sentences about facts).

Selected Methods of Rejecting Arguments for Determinism in Tense Logic Systems

Abstract In this article we will consider the application of tense logics enriched with additional modal operators or additional logical values to construct logical systems in which the thesis of logical determinism cannot be expressed.

Overcoming the "valleys of death" in advanced therapies: The role of finance.

Advanced therapies are the frontier of medical research and have a relevant therapeutic potential and a profound social value. Despite this, their funding is hindered by many heterogeneous factors that obstruct their translation and survival on the market, even when approved and effective. Using an extensive bibliometric and systematic review of 174 articles published between 2001 and 2023, this study aims to identify the factors hindering the financing of advanced therapies and suggest future research lines to overcome the biomedical and economic "valleys of death". This study is the first review focused on advanced therapies from a financial perspective, and it contributes to advancing scientific knowledge in several ways. First, it highlights that finance academics paid little attention to the topic and most of their contributions are now outdated; therefore, there is the need to explore the new opportunities and solutions offered by financial innovation and the application of new technologies to financial activity. Second, it asks for an interdisciplinary approach to exploring advanced therapies' barriers from a holistic and process perspective and exploiting the social value generated by the development of innovative therapies. Finally, it analyzes the obstacles and value destroyed by the absence of an organic and coordinated process of public intervention, underscoring the imperative for further research to explore new public-private financial models and risk-sharing schemes and extend evaluation models by integrating financial and social value logic.

How breakthrough innovations develop in an organization with logic multiplicity: A multiple case study of a healthcare organization in China

Despite recognizing the strategic importance of breakthrough innovations (BIs) and changing organizational landscapes toward multifaceted values, the question of how BIs emerge and develop in organizations that exhibit multifaceted value logics remains largely unanswered. To address this gap, we investigate the underlying rationale (i.e. logic interplay) of the organizational mechanisms that contribute to the emergence and development of BI practices under logic multiplicity from the perspective of institutional logic. By conducting in-depth case studies of three breakthrough innovation projects in the context of a prominent Chinese healthcare organization that is characterized by the presence of multiple logics, we identify a process model for BI development under logic multiplicity. The model contains three sequential mechanisms associated with logic interplay—logic-bridging, logic-harmonizing, and logic-tilting—that subsequently contribute to specific BI practices across different stages of the BI development process. Our process model illustrates how organizations with multiple logics facilitate the evolution of BIs, emphasizes the interplay and coevolution of diverse logics and highlights the agency of organizational actors in this context.

Presuppositions and the Content Implication

In the 1950s Peter Strawson analyzed the works of Bertrand Russell regarding fundamental definitions of meaning, sentences and truth value. The debate between them uncovered many issues that Fregean, truth-functional logics have when defining concepts from natural language. To reconcile the Fregean paradigm with the reality of language use, Strawson proposed the concept of presuppositions  necessary preconditions for the truth of other sentences. We believe that his proposition stemmed primarily from the problem caused by the fact that Fregean, truth-functional logics are not sensitive to the contents of sentences and reduce them to their logical values. This is bound to produce a mismatch between the way logic models reasoning and the way language users reason since real-life reasoning is performed on the contents of sentences and not their logical values. Inspired by the ideas of Strawson and Roman Suszko, who initiated the paradigm of non-Fregean logics, we propose a new solution to the debate between Strawson and Russell. In our solution, the content implication connective is used to express content relations between sentences. We move away from truth and falsehood as the sole two semantic correlates of sentences and instead work in a system where the contents of sentences are their semantic correlates.

Ultralow-energy multiferroic majority gates via magnetostrictive heterogeneity

Multiferroic nanomagnetic technology represents a cutting-edge domain with considerable potential for advancing the frontier of ultra-low energy, high precision, and swift responsive nanomagnetic nonvolatile logic gates. This manuscript introduces an innovative majority logic gate that capitalizes on the disparate magnetostrictive responses of materials with positive and negative coefficients under uniform strain conditions, through the implementation of a heterogeneous multiferroic structure integrated with a strain clocking mechanism. Distinct from traditional nanomagnetic majority logic gates, which rely on a single material within a stairs-type global strain clocking paradigm, our proposed design realizes an order-of-magnitude reduction in energy dissipation per operational cycle. Furthermore, simulate each scenario in a thermal noise field, with different logic value inputs getting the correct output, the majority gate supports pipelining capabilities, and offers significant insights for the engineering of energy-efficient multiferroic nanomagnetic logic devices.