Related papers: Modular Multiplication without Carry Propagation (…

This paper presents arithmetic operations like addition, subtraction and multiplications in Modulo-4 arithmetic, and also addition, multiplication in Galois field, using multi-valued logic (MVL). Quaternary to binary and binary to…

Boolean neural networks offer hardware-efficient alternatives to real-valued models. While quantization is common, purely Boolean training remains underexplored. We present a practical method for purely Boolean backpropagation for networks…

In this note, we construct and study an algebraic system similar to the natural numbers, but with noncommutative addition. The addition we introduce is a binary operation that commutes with itself in the sense of N. Durov. Neverheless, the…

A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…

Motivated by cryptographic applications, we investigate two machine learning approaches to modular multiplication: namely circular regression and a sequence-to-sequence transformer model. The limited success of both methods demonstrated in…

Existing approaches to combine both additive and multiplicative neural units either use a fixed assignment of operations or require discrete optimization to determine what function a neuron should perform. However, this leads to an…

We present a simulation algorithm that accurately propagates a molecule pair using large time steps without the need to invoke the full exact analytical solutions of the Smoluchowski diffusion equation. Because the proposed method only uses…

Parallel addition, i.e., addition with limited carry propagation, has been so far studied for complex bases and integer alphabets. We focus on alphabets consisting of integer combinations of powers of the base. We give necessary conditions…

We present a non-commutative algorithm for multiplying 5x5 matrices using 99 multiplications. This algorithm is a minor modification of Makarov's algorithm which exhibit the previous best known bound with 100 multiplications.

We show how one can use non-prime-power, composite moduli for computing representations of the product of two $n\times n$ matrices using only $n^{2+o(1)}$ multiplications.

A new algorithm for estimating the fraction of numbers that is present in a superpositional state which satisfies a given condition,is introduced.This algorithm is conceptually simple and does not require quantum Fourier transform.Also the…

This brief addresses the problem of implementing very large constant multiplications by a single variable under the shift-adds architecture using a minimum number of adders/subtractors. Due to the intrinsic complexity of the problem, we…

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:…

In this note, we extend modular techniques for computing Gr\"obner bases from the commutative setting to the vast class of noncommutative $G$-algebras. As in the commutative case, an effective verification test is only known to us in the…

We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform several modular operations with machine integer or floating point…

Multiple Constant Multiplication (MCM) over integers is a frequent operation arising in embedded systems that require highly optimized hardware. An efficient way is to replace costly generic multiplication by bit-shifts and additions, i.e.…

This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…

The quest for non-commutative matrix multiplication algorithms in small dimensions has seen a lot of recent improvements recently. In particular, the number of scalar multiplications required to multiply two $4\times4$ matrices was first…

Multiplication of polynomials is among key operations in computer algebra which plays important roles in developing techniques for other commonly used polynomial operations such as division, evaluation/interpolation, and factorization. In…

Matrix factorization is a common machine learning technique for recommender systems. Despite its high prediction accuracy, the Bayesian Probabilistic Matrix Factorization algorithm (BPMF) has not been widely used on large scale data because…