Related papers: Ternary circuits: why R=3 is not the Optimal Radix…

Any system that is used for naming or representing numbers is a number system, also known as numeral system. The modern civilization is familiar with decimal number system using ten digits. However digital devices and computers use binary…

By a (latin) unitrade, we call a set of vertices of the Hamming graph that is intersects with every maximal clique in $0$ or $2$ vertices. A bitrade is a bipartite unitrade, that is, a unitrade splittable into two independent sets. We study…

Triple Modular Redundancy (TMR) has been traditionally used to ensure complete tolerance to a single fault or a faulty processing unit, where the processing unit may be a circuit or a system. However, TMR incurs more than 200% overhead in…

Matrix computation is ubiquitous in modern scientific and engineering fields. Due to the high computational complexity in conventional digital computers, matrix computation represents a heavy workload in many data-intensive applications,…

The reversible circuit synthesis problem can be reduced to permutation group. This allows Schreier-Sims Algorithm for the strong generating set-finding problem to be used to find tight bounds on the synthesis of 3-bit reversible circuits…

Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…

During the course of the last decade, traveling wave accelerating structures for a future Linear Collider have been the object of intense R&D efforts. An important problem is the efficient computation of the long range wakefield with the…

One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing on QC codes…

Analysis of the convergence rates of modern convex optimization algorithms can be achived through binary means: analysis of emperical convergence, or analysis of theoretical convergence. These two pathways of capturing information diverge…

This paper explores whether or not a complete ternary full adder, whose input variables can independently be '0', '1', or '2', is indispensable in the arithmetic blocks of adder, subtractor, and multiplier. Our investigations show that none…

Recently, we proposed a novel transistor architecture for 3D stacked FETs called Flip FET (FFET), featuring N/P transistors back-to-back stacked and dual-sided interconnects. With dual-sided power rails and signal tracks, FFET can achieve…

Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, by F\"{u}rer, shows that two $n$-bit numbers can be multiplied via a boolean circuit of size $O(n \lg…

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require…

Nanomechanical systems have been proposed as an alternative computing platform for high radiation environments, where semiconductor electronics traditionally fail, as well as to allow improved gate densities and energy consumption. While…

While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…

Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in simple situations. This paper concerns binary radix systems, i.e., positional number systems with digits…

Low-bit quantized neural networks are of great interest in practical applications because they significantly reduce the consumption of both memory and computational resources. Binary neural networks are memory and computationally efficient…

Basic logic gates and their operations in ternary quantum domain are involved in the synthesis of ternary quantum circuits. Only a few works define ternary algebra for ternary quantum logic realization. In this paper, a ternary logic…

Binary LDPC coded relay systems have been well studied previously with the assumption of infinite codeword length. In this paper, we deal with non-binary LDPC codes which can outperform their binary counterpart especially for practical…

A maximal repetition, or run, in a string, is a maximal periodic substring whose smallest period is at most half the length of the substring. In this paper, we consider runs that correspond to a path on a trie, or in other words, on a…