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This paper investigates the potentials of using a hybrid memristor CMOS technology, called MeMOS, for the realisation of ternary adders. Ternary adders exploit the qualitative advantage of multi-value storage capability of memristors…

An integer $n$ is said to be ternary if it is composed of three distinct odd primes. In this paper, we asymptotically count the number of ternary integers $n \leq x$ with the constituent primes satisfying various constraints. We apply our…

Many approaches for verifying input-output properties of neural networks have been proposed recently. However, existing algorithms do not scale well to large networks. Recent work in the field of model compression studied binarized neural…

The design of balanced ternary digital logic circuits based on memristors and conventional CMOS devices is proposed. First, balanced ternary minimum gate TMIN, maximum gate TMAX and ternary inverters are systematically designed and verified…

Non-volatile memory (NVM) crossbars have been identified as a promising technology, for accelerating important machine learning operations, with matrix-vector multiplication being a key example. Binary neural networks (BNNs) are especially…

Ordinary binary multiplication of natural numbers can be generalized in a non-trivial way to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of `3-primality' -- primality with…

A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…

Quantization is widely applied in machine learning to reduce computational and storage costs for both data and models. Considering that classification tasks are fundamental to the field, it is crucial to investigate how quantization impacts…

In this work faster unsigned multiplication has been achieved by using a combination of High Performance Multiplication [HPM] column reduction technique and implementing a N-bit multiplier using 4 N/2-bit multipliers (recursive…

Similarity comparisons of the form "Is object a more similar to b than to c?" are useful for computer vision and machine learning applications. Unfortunately, an embedding of $n$ points is specified by $n^3$ triplets, making collecting…

The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…

Non-Trivial Reversible Identities (NTRIs) are reversible circuits that have equal inputs and outputs. NTRIs cannot be detected using optimization algorithms in the literature. Existence of NTRIs in a circuit will cause a slow down by…

Ternary logic is expected to increase the area efficiency of VLSI due to its expressiveness compared to the traditional binary logic. This paper proposes a new symmetric ternary logic and a systematic logic composition methodology that…

Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required…

In-memory associative processor architectures are offered as a great candidate to overcome memory-wall bottleneck and to enable vector/parallel arithmetic operations. In this paper, we extend the functionality of the associative processor…

Today's PCs can directly manipulate numbers not longer than 64 bits because the size of the CPU registers and the data-path are limited. Consequently, arithmetic operations such as addition, can only be performed on numbers of that length.…

While binary neural networks (BNNs) offer significant benefits in terms of speed, memory and energy, they encounter substantial accuracy degradation in challenging tasks compared to their real-valued counterparts. Due to the binarization of…

Binary addition is one of the most primitive and most commonly used applications in computer arithmetic. A large variety of algorithms and implementations have been proposed for binary addition. Huey Ling proposed a simpler form of CLA…

We present a necessary and sufficient condition for a 3 by 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 by 3 matrix can be tested. This test generalizes to a…

Ternary Neural Networks (TNNs) have received much attention due to being potentially orders of magnitude faster in inference, as well as more power efficient, than full-precision counterparts. However, 2 bits are required to encode the…