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The purpose of this paper is to examine the structural and computational potentials of a powerful class of neural networks (NNs), called multiple-valued logic neural networks (MVLNN), for predicting the behavior of phenomenological systems with highly nonlinear dynamics. MVLNNs are constructed based on the integration of a number of neurons working based on the principle of multiple-valued logics. MVLNNs possess some particular features, namely complex-valued weights, input, and outputs coded by kth roots of unity, and a continuous activation as a mean for transferring numbers from complex spaces to trigonometric spaces, which distinguish them from most of the existing NNs.

The presented study can be categorized into three sections. At the first part, the authors attempt at providing the mathematical formulations required for the implementation of ARX-based MVLNN (AMVLNN). In this context, it is indicated that how the concept of ARX can be used to revise the structure of MVLNN for online applications. Besides, the stepwise formulation for the simulation of Chua’s oscillatory map and multiple-valued logic-based BP are given. Through an analysis, some interesting characteristics of the Chua’s map, including a number of possible attractors of the state and sequences generated as a function of time, are given.

Based on a throughout simulation as well as a comprehensive numerical comparative study, some important features of AMVLNN are demonstrated. The simulation results indicate that AMVLNN can be employed as a tool for the online identification of highly nonlinear dynamic systems. Furthermore, the results show the compatibility of the Chua’s oscillatory system with BP for an effective tuning of the synaptic weights. The results also unveil the potentials of AMVLNN as a fast, robust, and efficient control-oriented model at the heart of NMPC control schemes.

This study presents two innovative propositions. First, the structure of MVLNN is modified based on the concept of ARX system identification programming to suit the base structure for coping with chaotic and highly nonlinear systems. Second, the authors share the findings about the learning characteristics of MVLNNs. Through an exhaustive comparative study and considering different rival methodologies, a novel and efficient double-stage learning strategy is proposed which remarkably improves the performance of MVLNNs. Finally, the authors describe the outline of a novel formulation which prepares the proposed AMVLNN for applications in NMPC controllers for dynamic systems.

The purpose of this paper is to introduce an approach for m‐valued classical and non‐classical (reversible and quantum) optical computing. The developed approach utilizes new multiplexer‐based optical devices and circuits within switch logic to perform the required optical computing. The implementation of the new optical devices and circuits in the optical regular logic synthesis using new lattice and systolic architectures is introduced, and the extensions to quantum optical computing are also presented.

The new linear optical circuits and systems utilize coherent light beams to perform the functionality of the basic logic multiplexer. The 2‐to‐1 multiplexer is a basic building block in switch logic, where in switch logic a logic circuit is implemented as a combination of switches rather than a combination of logic gates as in the gate logic, which proves to be less‐costly in synthesizing wide variety of logic circuits and systems. The extensions to quantum optical computing using photon spins and the collision of Manakov solitons are also presented.

New circuits for the optical realizations of m‐valued classical and reversible logic functions are introduced. Optical computing extensions to linear quantum computing using photon spins and nonlinear quantum computing using Manakov solitons are also presented. Three new multiplexer‐based linear optical devices are introduced that utilize the properties of frequency, polarization and incident angle that are associated with any light‐matter interaction. The hierarchical implementation of the new optical primitives is used to synthesize regular optical reversible circuits such as the m‐valued regular optical reversible lattice and systolic circuits. The concept of parallel optical processing of an array of input laser beams using the new multiplexer‐based optical devices is also introduced. The design of regular quantum optical systems using regular quantum lattice and systolic circuits is introduced. New graph‐based quantum optical representations using various types of quantum decision trees are also presented to efficiently represent quantum optical circuits and systems.

The introduced methods for classical and non‐classical (reversible and quantum) optical regular circuits and systems are new and interesting for the design of several future technologies that require optimal design specifications such as super‐high speed, minimum power consumption and minimum size such as in quantum computing and nanotechnology.

This paper is a survey and classification of a number of factors that relate directly to cost in the computer engineering design of arithmetic units. The general factors considered are inputs, gates, thresholds, algebras, inputs versus gates, values, reliability, implementability, and complexity. The paper contains some recent logic calculations by the author on gate versus input counts and reduction of complexity in the case of ternary logic.

The purpose of this paper is to introduce new implementations for parallel processing applications using bijective systolic networks and their corresponding carbon-based field emission controlled switching. The developed implementations are performed in the reversible domain to perform the required bijective parallel computing, where the implementations for parallel computations that utilize the presented field-emission controlled switching and their corresponding many-valued (m-ary) extensions for the use in nano systolic networks are introduced. The second part of the paper introduces the implementation of systolic computing using two-to-one controlled switching via carbon-based field emission that were presented in the first part of the paper, and the computational extension to the general case of many-valued (m-ary) systolic networks utilizing many-to-one carbon-based field emission is also introduced.

The introduced systolic systems utilize recent findings in field emission and nano applications to implement the functionality of the basic bijective systolic network. This includes many-valued systolic computing via field-emission techniques using carbon-based nanotubes and nanotips. The realization of bijective logic circuits in current and emerging technologies can be very important for various reasons. The reduction of power consumption is a major requirement for the circuit design in future technologies, and thus, the new nano systolic circuits can play an important role in the design of circuits that consume minimal power for future applications such as in low-power signal processing. In addition, the implemented bijective systems can be utilized to implement massive parallel processing and thus obtaining very high processing performance, where the implementation will also utilize the significant size reduction within the nano domain. The extensions of implementations to field emission-based many-valued systolic networks using the introduced bijective nano systolic architectures are also presented.

Novel bijective systolic architectures using nano-based field emission implementations are introduced in this paper, and the implementation using the general scheme of many-valued computing is presented. The carbon-based field emission implementation of nano systolic networks is also introduced. This is accomplished using the introduced field-emission carbon-based devices, where field emission from carbon nanotubes and nano-apex carbon fibers is utilized. The implementations of the many-valued bijective systolic networks utilizing the introduced nano-based architectures are also presented.

The introduced bijective systolic implementations form new important directions in the systolic realizations using the newly emerging nano-based technologies. The 2-to-1 multiplexer is a basic building block in “switch logic,” where in switch logic, a logic circuit is realized as a combination of switches rather than a combination of logic gates as in the gate logic, which proves to be less costly in synthesizing multiplexer-based wide variety of modern circuits and systems since nano implementations exist in very compact space where carbon-based devices switch reliably using much less power than silicon-based devices. The introduced implementations for nano systolic computation are new and interesting for the design in future nanotechnologies that require optimal design specifications of minimum power consumption and minimum size layout such as in low-power control of autonomous robots and in the adiabatic low-power VLSI circuit design for signal processing applications.

The introduced bijective systolic implementations form new important directions in the systolic realizations utilizing the newly emerging nanotechnologies. The introduced implementations for nano systolic computation are new and interesting for the design in future nanotechnologies that require optimal design specifications of high performance, minimum power and minimum size.

The purpose of this paper is to develop a new mathematical method for the reliability analysis and evaluation of multi-state system (MSS) reliability that agrees with specifics of such system. It is possible based on the application of multiple-valued logic (MVL) that is a natural extension of Boolean algebra used in reliability analysis.

Similar to Boolean algebra, MVL is used for the constriction of the structure function of the investigated system. The interpretation of the structure function of the MSS in terms of MVL allows using mathematical methods and approaches of this logic for the analysis of the structure function.

The logical differential calculus is one of mathematical approaches in MVL. The authors develop new method for MSS reliability analysis based on logical differential calculus, in particular direct partial logical derivatives, for the investigation of critical system states (CSSs). The proposed method allows providing the qualitative and quantitative analyses of MSS: the CSS can be defined for all possible changes of any system component or group of components, and probabilities of this state can also be calculated.

The proposed method permits representing the MSS in the form of a structure function that is interpreted as MVL function and provides the system analyses without special transformation into Boolean interpretation and with acceptable computational complexity.

The purpose of this paper is to introduce new implementations for parallel processing applications using bijective systolic networks and the corresponding carbon-based field emission controlled switching. The developed implementations are performed in the reversible domain to perform the required bijective parallel computing, where the implementations for parallel computations that utilize the presented field-emission controlled switching and their corresponding m-ary (many-valued) extensions for the use in nano systolic networks are introduced. The first part of the paper presents important fundamentals with regards to systolic computing and carbon-based field emission that will be utilized in the implementations within the second part of the paper.

The introduced systolic systems utilize recent findings in field emission and nano applications to implement the functionality of the basic bijective systolic network. This includes many-valued systolic computing via field emission techniques using carbon-based nanotubes and nanotips. The realization of bijective logic circuits in current and emerging technologies can be very important for various reasons. The reduction of power consumption is a major requirement for the circuit design in future technologies, and thus, the new nano systolic circuits can play an important role in the design of circuits that consume minimal power for future applications such as in low-power signal processing. In addition, the implemented bijective systems can be utilized to implement massive parallel processing and thus obtaining very high processing performance, where the implementation will also utilize the significant size reduction within the nano domain. The extensions of implementations to field emission-based many-valued systolic networks using the introduced bijective nano systolic architectures are also presented.

Novel bijective systolic architectures using nano-based field emission implementations are introduced in this paper, and the implementation using the general scheme of many-valued computing is presented. The carbon-based field emission implementation of nano systolic networks is also introduced. This is accomplished using the introduced field emission carbon-based devices, where field emission from carbon nanotubes and nano-apex carbon fibers is utilized. The implementations of the many-valued bijective systolic networks utilizing the introduced nano-based architectures are also presented.

The introduced bijective systolic implementations form new important directions in the systolic realizations using the newly emerging nano-based technologies. The 2-to-1 multiplexer is a basic building block in “switch logic,” where in switch logic, a logic circuit is realized as a combination of switches rather than a combination of logic gates as in the gate logic, which proves to be less costly in synthesizing multiplexer-based wide variety of modern circuits and systems since nano implementations exist in very compact space where carbon-based devices switch reliably using much less power than silicon-based devices. The introduced implementations for nano systolic computation are new and interesting for the design in future nanotechnologies that require optimal design specifications of minimum power consumption and minimum size layout such as in low-power control of autonomous robots and in the adiabatic low-power very-large-scale-integration circuit design for signal processing applications.

Ant Colony Optimization and Particle Swarm Optimization represent two widely used Swarm Intelligence (SI) optimization techniques. Information processing using Multiple-Valued Logic (MVL) is carried out using more than two discrete logic levels. In this paper, we compare two the SI-based algorithms in synthesizing MVL functions. A benchmark consisting of 50,000 randomly generated 2-variable 4-valued functions is used for assessing the performance of the algorithms using the benchmark. Simulation results show that the PSO outperforms the ACO technique in terms of the average number of product terms (PTs) needed. We also compare the results obtained using both ACO-MVL and PSO-MVL with those obtained using Espresso-MV logic minimizer. It is shown that on average, both of the SI-based techniques produced better results compared to those produced by Espresso-MV. We show that the SI-based techniques outperform the conventional direct-cover (DC) techniques in terms of the average number of product terms required.

It is well known that the only way of making complexity in inductive (data‐driven) systems modelling manageable is to be tolerant of predictive (or retrodictive) uncertainty in the resulting models. It is argued that two complementary principles — the principles of maximum and minimum uncertainty — are essential to using uncertainty properly to combat complexity. When uncertainty is conceptualised in terms of probability theory, these principles become the well‐established principles of maximum and minimum entropy. When a more general framework of fuzzy measures is employed, uncertainty becomes a multi‐dimensional entity and the maximum and minimum uncertainty principles lead to optimisation problems with multiple objective criteria. Four distinct types of uncertainty are now recognised and their well‐justified measures determined within fuzzy set theory and one subset of fuzzy measures — the Dempster‐Shafer theory of evidence. The uncertainty types and their measures are briefly described.

Examines the ability of an expert computer system to evaluate uncertainty within a valuation context and thus emulate the professional skill of the valuer. Shows that because property valuation programs based on regression analysis require data input for each variable, they are unable to evaluate uncertainty and hence to apply the rational judgement which enables the human valuer to produce a valuation in the light of uncertain or incomplete information.