Related papers: Arithmetic Operations in Multi-Valued Logic

We consider an example of four valued semantics partially inspired by quantum computations and negation-like operations occurred therein. In particular we consider a representation of so called square root of negation within this four…

A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one…

For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the…

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…

Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for…

Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic:…

Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a…

We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…

Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…

In this paper, we have proposed a novel VLSI-oriented approach to computing the rotation matrix entries from the quaternion coefficients. The advantage of this approach is the complete elimination of multiplications and replacing them by…

We present master formulas for the divergent part of the one-loop effective action for an arbitrary (both minimal and nonminimal) operators of any order in the 4-dimensional curved space. They can be considered as computer algorithms,…

In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…

A logical system derived from linear logic and called QMLL is introduced and shown able to capture all unitary quantum circuits. Conversely, any proof is shown to compute, through a concrete GoI interpretation, some quantum circuits. The…

We present some basic integer arithmetic quantum circuits, such as adders and multipliers-accumulators of various forms, as well as diagonal operators, which operate on multilevel qudits. The integers to be processed are represented in an…

In this study, we constructed a primitive quantum arithmetic logic unit (qALU) based on the quantum Fourier transform. The qALU is capable of performing arithmetic ADD (addition) and logic NAND gate operations. We presented two versions of…

Closed form expressions for a logarithm of general multivector (MV) in base-free form in real geometric algebras (GAs) Cl(p,q) are presented for all n=p+q=3. In contrast to logarithm of complex numbers (isomorphic to Cl(0,1), 3D logarithmic…

Multiplication is indispensable and is one of the core operations in many modern applications including signal processing and neural networks. Conventional right-to-left (RL) multiplier extensively contributes to the power consumption, area…

We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be performed by combinational logic networks with linear size…

A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…

Finite field multiplier is mainly used in error-correcting codes and signal processing. Finite field multiplier is regarded as the bottleneck arithmetic unit for such applications and it is the most complicated operation over finite field…