This paper presents a novel and successful logic synthesis method for optimizing ternary logic functions of any given number of input variables. A new optimization algorithm to synthesize and minimize an arbitrary ternary logic function of n-input variables can always lead this function to optimal or very close to optimal solution, where [n (n1)/2]1 searches are necessary to achieve the optimal solution. Therefore, the complexity number of this algorithm has been greatly reduced from O(3n) into O(n2). The advantages of this synthesis and optimization algorithm are: (1) Very easy logic synthesis method. (2) Algorithm complexity is O(n2). (3) Optimal solution can be obtained in very short time. (4) The method can solve the interconnection problems (interconnection delay) of VLSI and ULSI processors, where very fast and parallel operations can be achieved. A transformation method between operational and polynomial domains of ternary logic functions of n-input variables is also discussed. This transformation method is very effective and simple. Design of the circuits of GF(3) operators, addition and multiplication mod-3, have been proposed, where these circuits are composed of Josephson junction devices. The simulation results of these circuits and examples show the following advantages: very good performances, very low power consumption, and ultra high speed switching operation.

In this paper, a fault model for multiple-valued programmable logic arrays (MV-PLAs) is proposed and the equivalences of faults of MV-PLA's are discussed. In a supposed multiple-valued NOR/TSUM PLA model, it is shown that multiple-valued stuck-at faults, multiple-valued bridging faults, multiple-valued threshold shift faults and other some faults in a literal generator circuit are equivalent or subequivalent to a multiple crosspoint fault in the NOR plane or a multiple fault of weights in the TSUM plane. These results lead the fact that multiple-valued test vector set which indicates all multiple crosspoint fault and all multiple fault of weights also detects above equivalent or subequivalent faults in a MV-PLA.

This paper proposes a repairable and diagnosable k-valued cellular array. We assume a single fault, i.e., either stuck-at-O fault or stuck-at-(k1) fault of switches occurs in the array. By building in a duplicate column iteratively, when a stuck-at-(k1) fault occurs in the array, the fault never influences the output of the array. That is, we can construct a fault-tolerant array for the stuck-at-(k1) fault. While, for the stuck-at-O fault, the diagnosing method is simple and easy because we don't have to diagnose the stuck-at-(k1) fault. Moreover, our array can be repaired easily for the fault. The comparison with other rectangular arrays shows that our array has advantages for the number of cells and the cost of the fault diagnosis.

This paper presents a low-power 8-valued cellular array VLSI for high-speed image processing based on logical neighborhood operations with 33 windows. This array is useful for performing low-level image processing such as noise removal and edge detection, in intelligent integrated systems where immediate response to input change as well as high throughput is needed. In order to achieve high-speed image processing, template matching for neighborhood operations can be performed in parallel on each row. Each row of the image is operated in a pipelining manner. The direct 8-valued encoding of the matched results for three different 33 masks makes it possible to reduce the number of operations by one-third. In the hardware implementation, the matching cell for logical neighborhood operations can be implemented compactly using MOS transistors with different threshold voltage, which are programmed by multiple ion implants. Moreover, a new literal circuit for detecting multiple-valued signals using a dynamic design style eliminates hazards due to timing skews in the difference of various input voltage levels, so that the dynamic power dissipation of the proposed circuit is greatly reduced. Finally, it is demonstrated that the processing time of the proposed cellular array is reduced to about 40 percent in comparison with that of a corresponding binary circuit when power dissipation/area = 0.3 W/100 mm2.

Truncated sum (TSUM for short) is useful for MV-PLA's realization. This paper introduces a new class of multiple-valued logic functions that are expressed by truncated sum, differential product (DPRODUCT for short), NOT and variables, where TSUM (x, y)min (xy, p1) and DPRODUCT (x, y)max (xy(p1), 0) is newly defined as the product that is derived by applying De Morgan's laws to TSUM. We call the functions T-functios. First, this paper clarifies that a set of T-functions is not a lattice. It clarifies that Lukasiewicz implication can be expressed by TSUM and NOT. It guarantees that a set of p-valued T-functios is not complete but complete with constants. Next, the speculations of the number of T-functions for less than ten radixes are derived. For eleven or more radix p, a speculation of the number of p-valued T-functions is shown. Moreover, it compares the T-functions with B-functions. The B-functions have been defined as the functions expressed by MAX, MIN, NOT and variables. As a result, it shows that a set of T-functions includes a set of B-functions. Finally, an inclusion relation among these functional sets and normality condition is shown.

This paper presents a high-density multiple-valued content-addressable memory (MVCAM) based on a floating-gate MOS device. In the proposed CAM, a basic operation performed in each cell is a threshold function that is a kind of inverter whose threshold value is programmable. Various multiple-valued operations for data retrieval can be easily performed using threshold functions. Moreover, each cell circuit in the MVCAM can be implemented using only a single floating-gate MOS transistor. As a result, the cell area of the four-valued CAM are reduced to 37% in comparison with that of the conventional dynamic CAM cell.

A new circuit design of Josephson ternary δ-gate composed of Josephson junction devices is presented. Mathematical theory for synthesizing, analyzing, and realizing any given function in ternary system using Josephson ternary δ-gate is introduced. The Josephson ternary δ-gate is realized using SQUID technique. Circuit simulation results using J-SPICE demonstrated the feasibility and the reliability operations of Josephson ternary δ-gate with very high performances for both speed and power consumption (max. propagation delay time44 ps and max. power consumption2.6µW). The Josephson ternary δ-gate forms a complete set (completeness) with the ternary constants (1, 0, 1). The number of SQUIDs that are needed to perform the operation of δ-gate is 6. Different design with less than 6 SQUIDs is not possible because it can not perform the operation of δ-gate. The advantages of Josephson ternary δ-gate compared with different Josephson logic circuits are as follows: The δ-gate has the property that a simple realization to any given ternary logic function as the building blocks can be achieved. The δ-gate has simple construction with small number of SQUIDs. The δ-gate can realize a large number of ternary functions with small number of input/output pins. The performances of δ-gate is very high, very low power consumption and ultra high speed switching operation.

This paper proposes new architecture LSIs based on wave-parallel computing to provide an essential solution to the interconnection problems in massively parallel processing. The basic concept is ferquency multiplexing of digital information, which enables us to utilize the parallelism of electrical (or optical) waves for parallel processing. This wave-parallel computing concept is capable of performing several independent binary funtions in parallel with a single module. In this paper, we discuss the design of wave-parallel image processing LSI to demonstrate the feasibility of reducing the number of interconnections among modules.

This review presents research topics and results on digital signal processing in the last twenty years in Japan. The main parts of the review consist of design and analysis of multidimensional digital filters, multiple-valued logic circuits and number systems for signal processing, and general purpose signal processors.

Recently, fuzzy logic which is a kind of infinite multiple-valued logic has been studied to treat certain ambiguities, and its algebraic properties have been studied by the name of fuzzy logic functions. In order to treat modality (necessity, possibility) in fuzzy logic, which is an important concept of multiple-valued logic, the intuitionistic logical negation is required in addition to operations of fuzzy logic. Infinite multiple-valued logic functions introducing the intuitionistic logical negation into fuzzy logic functions are called Kleene-Stone logic functions, and they enable us to treat modality. The domain of modality in which Kleene-Stone logic functions can handle, however, is too limited. We will define α-KS logic functions as infinite multiple-valued logic functions using a unary operation instead of the intuitionistic logical negation of Kleene-Stone logic functions. In α-KS logic functions, modality is closer to our feelings. In this paper we will show some algebraic properties of α-KS logic functions. In particular we prove that any n-variable α-KS logic function is determined uniquely by all inputs of 7 values which are 7 specific truth values of the original infinite truth values. This means that there is a bijection between the set of α-KS logic functions and the set of 7-valued α-KS logic functions which are restriction of α-KS logic functions to 7 specific truth values. Finally, we show a necessary and sufficient condition for a 7-valued logic function to be a 7-valued α-KS logic function.

This paper presents Bi-CMOS current-mode multiple valued logic circuit with 1.5 V supply voltage. This circuit is composed of current mirror, threshold detector and current source. This circuit has advantages such as high accuracy, high speed, high density and low supply voltage. So, it is possible to realize high-radix multiple valued logic circuit. As an other application of the proposed circuit, a processing unit of fuzzy inference is given. This circuit operates with high speed and high accuracy. The circuit simulation of the proposed circuit has been performed using SPICE2 program.

A new computer architecture using multiwavelength optoelectronic integrated circuits (OEICs) is proposed to attack the problems caused by interconnection complexity. Multiwavelength-OEIC architecures, where various wavelengths are employed as information carriers, provide the wavelength as an extra dimension of freedom for parallel processing, so that we can perform several independent computations in parallel in a single optical module using the wavelength space. This multiplex computing" enables us to reduce the wiring area required by a network and improve their complexity. In this paper, we discuss the efficient multiplexing of Batcher's bitonic sorting networks, highly parallel computing architectures that require global interconnections inherently. A systematic multiplexing of interconnection topology is presented using a binary representation of the connectivities of interconnection paths. It is shown that the wiring area can be reduced by a factor of 1/r2 using r kinds of wavelength components.

This paper first clarifies the logic construction of safety control for the operation of a power press and then describes fail-safe dual two-rail system signal processing and fail-safe multiple-valued logic operations as methods for achieving this control as a fail-safe system. It finally shows a circuit for generating fail-safe two-rail run button signals based on ternary logic for concrete operation of the power press and an operation control circuit for confirming brake performance for each cycle of slide operation by using the run button signals. The control circuit uses such multiple-valued logic operations that binary logic signals that do not erroneously go logic 1 are added to a multiple-valued logic signal and the multiple-valued logic signal is converted to a binary logic signal that does not erroneously go logic 1 by a threshold operation.

A method is proposed for realizing any k-valued n-variable function with a celluler array, which consists of linear arrays (called input arrays) and a rectangular array (called control array). In this method, a k-valued n-variable function is divided into kn-1 one-variable functions and remaining (n1)-variable function. The parts of one-variable functions are realized by the input arrays, remaintng the (n1)-variable function is realized by the control array. The array realizing the function is composed by connecting the input arrays with the control array. Then, this array requires (kn2)kn-1 cells and the number is smaller than the other rectangular arrays. Next, a ternary cell circuit and a literal circuit are actually constructed with CMOS transistors and NMOS pass transistors. The experiment shows that these circuits perform the expected operations.

The evolution of Multiple-Valued Logic (MVL) circuits has been inexorably tied to the rapid technological changes induced by evolving needs and emerging developments in computing methodologies. Unfortunately for MVL, the numbers of designers of technologies and circuits whose lives are dedicated to the improvement of binary techniques, are large and overwhelming. Correspondingly, technological developments in MVL typically await the appearance of a problem or technique in the larger binary world to motivate and/or make possible some new advance. Such opportunities are inevitably quite transient since each such problem is simultaneously attacked by many others of a more conventional bent, and, as well, each technological change begets yet another, quickly. It is in the sensing of this reality that the present paper is written. Correspondingly, its thrust is two-fold: One target is the possibility of encouraging a leap ahead through modest technological projection. The other is the possibility of identifying application areas that already exist in this unbalanced competition, but which are specially suited to multiple-valued solutions. For example, it has been clear for decades that one such area is that of arithmetic. Correspondingly, we in MVL must strive quickly to concentrate our efforts on applications that exploit such demonstrable strengths. Some such applications are includes here; others are visible historically, many probably remain to be found: Search on!

We have developed a new functional MOS transistor called Neuron MOSFET (abbreviated as neuMOS or νMOS) which simulates the function of biological neurons. The new transistor is capable of executing a weighted sum calculation of multiple input signals and threshold operation based on the result of weighted summation, all in the voltage mode at a single transistor level. By utilizing its neuron-like very powerful functional capability, various circuits essential for multiple-valued logic operation have been designed using quite simple circuit configurations. The circuit designs for data conversion between the multivalued and binary logic systems and for generating universal literal functions are described and their experimental verifications are presented. One of the most important features of νMOS multivalued lagic circuit is that the circuit operates basically in the voltage mode, thus greatly reducing the power dissipation as compared to the conventional current mode circuitry. This is indeed most essential in implementing multivalued logic systems in ultra large scale integration. Another important feature of νMOS design is in its flexibility of implementing logic functions. The functional form of a universal literal function, for instance, can be arbitrarily altered by external signals without any modifications in its hardware configuration. A circuit representing multiple-valued multithreshold functions is also proposed.

In this paper, a general theory on multiple-valued static random-access-memory (RAM) is investigated. A criterion for a stable and an unstable modes is proved with a strict mathematical method and expressed with a diagrammatic representation. Based on the theory, an NMOS 6-transistor ternary and a quaternary static RAM (SRAM) cells are proposed and simulated with PSPICE. The detail circuit design and realization are analyzed. A 10-valued CMOS current-mode static RAM cell is also presented and fabricated with standard 5-µm CMOS technology. A family of multiple-valued flip-flops is presented and they show to have desirable properties for use in multiple-valued sequential circuits. Both PSPICE simulations and experiments indicate that the general theory presented are very useful and effective tools in the optimum design and circuit realization of multiple-valued static RAMs and flip-flops.

This paper presents a VLSI-oriented arithmetic design method using a radix-2 redundant number representation with digit set {0, 1, 2} and multiple-valued current-mode (MVCM) circuit technology. We propose a carry-propagation-free (CPF) parallel addition method with redundant digit set {0, 1, 2} which is suitable for the design with MVCM circuits. Several types of CPF parallel adders are compared and the proposed CPF parallel adder with MVCM circuits offers the best total performance with respect to speed, complexity, and power dissipation. The designed basic arithmetic circuits has sufficient noise immunity to the supply voltage fluctuation which is important for stable operations of the VLSI circuits. The CPF parallel adder is effectively used as the reduction scheme of partial products in a high-speed compact multiplier. For example, the designed 3232 bit multiplier reduces the number of active elements to two-third and the number of interconnections to one-fifth of the corresponding binary Wallace tree multiplier, where the speed is almost the same. The structure is simple and regular. The static power dissipation of the designed 32-bit multiplier is estimated to be the mean value of 212 mW and the worst case of 708 mW. The total power including dynamic power dissipation would not be so large compared with that of the 32-bit binary CMOS multiplier reported under 10 MHz operation.

A fail-safe logic operation refers to such a processing operation that the output assumes the logical value zero when the operation circuit fails. The fail-safe multiple-valued logic operation is proposed as one method of logic operation. Section 2 defines the fail-asfe multiple-valued logic operation and presents an example of method for accomplishing the fail-safe multiple-valued logic operation. Section 3 describes the method of designing a fail-safe threshold operation device (window comparator) as basic device in the fail-safe multiple-valued logic operation in consideration of LSI implementation and shows an example of prototype fail-safe window comparator. This operation device has higher and lower thresholds. It oscillates and produces an operational output signal only when the input signal level falls between the higher and lower thresholds. Unless the fail-safe window comparator is supplied with input signals of higher voltage than the power supply voltage, it dose not form a feedbadk loop as required for it to oscillate. This characteristic prevents the device from erroneously producing an output signal when any failure occurs in the amplifiers comprising the oscillation circuit. The window comparator can be built as a fail-safe threshold operation device. The fail-safe characteristic is utilized in its LSI implementation. Section 4 verifies the fail-safe property of the prortotype fail-safe window comparator. It is shown that even when the LSI develops failures not evident from outsid (latent failures), it does not lose the operational function and maintains the fail-safe characteristic.

Kleene-Stone algebra is both Kleene algebra and Stone algebra. The set of Kleene-Stone logic functions discussed in this paper is one of the models of Kleene-Stone algebra, and they can easily represent the concepts of necessity and possibility which are important concepts for many-valued logic systems. Main results of this paper are that the followings are clarified: a necessary and sufficient condition for a function to be a Kleene-Stone logic function and a formula representing the number of n-variable Kleene-Stone logic functions.