Related papers: Determining Smallest Path Size of Multiplication T…
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…
In this paper the ensemble of codes formed by a serial concatenation of a repetition code with multiple accumulators connected through random interleavers is considered. Based on finite length weight enumerators for these codes, asymptotic…
As a generalization of the sum of digits function and other digital sequences, sequences defined as the sum of the output of a transducer are asymptotically analyzed. The input of the transducer is a random integer in $[0, N)$. Analogues in…
Functional transductions realized by two-way transducers (or, equally, by streaming transducers or MSO transductions) are the natural and standard notion of "regular" mappings from words to words. It was shown in 2013 that it is decidable…
We show some facts regarding the question whether, for any number $n$, the length of the shortest Addition Multiplications Chain (AMC) computing $n$ is polynomial in the length of the shortest division-free Straight Line Program (SLP) that…
We study matrix multiplication in the low-bandwidth model: There are $n$ computers, and we need to compute the product of two $n \times n$ matrices. Initially computer $i$ knows row $i$ of each input matrix. In one communication round each…
The class of regular transformations has several equivalent characterizations such as functional MSO transductions, deterministic two-way transducers, streaming string transducers, as well as regular transducer expressions (RTE). For…
This paper presents an efficient algorithm for the incremental construction of a minimal acyclic sequential transducer (ST) for a dictionary consisting of a list of input and output strings. The algorithm generalises a known method of…
Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…
Mathematical expressions were generated, evaluated and used to train neural network models based on the transformer architecture. The expressions and their targets were analyzed as a character-level sequence transduction task in which the…
Multiplication is a basic arithmetic operation that is encountered in almost all general-purpose microprocessing and digital signal processing applications, and multiplication is physically realized using a multiplier. This paper discusses…
The multiplicative depth of a logic network over the gate basis $\{\land, \oplus, \neg\}$ is the largest number of $\land$ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based…
Matrices are built and designed by applying procedures from lower order matrices. Matrix tensor products, direct sums or multiplication of matrices are such procedures and a matrix built from these is said to be a {\em separable} matrix. A…
A typical machine learning (ML) development cycle for edge computing is to maximise the performance during model training and then minimise the memory/area footprint of the trained model for deployment on edge devices targeting CPUs, GPUs,…
In arXiv:2204.03190, we proposed a universal method to reduce one-loop integrals with both tensor structure and higher-power propagators. But the method is quite redundant as it does not utilize the results of lower rank cases when…
Structured prompts require integrating components according to task-relevant relations. How a network implements this integration is often hard to judge in language or vision, where those relations are rarely specified precisely enough to…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
Transform coding is routinely used for lossy compression of discrete sources with memory. The input signal is divided into N-dimensional vectors, which are transformed by means of a linear mapping. Then, transform coefficients are quantized…
Many practical applications of optimal control are subject to real-time computational constraints. When applying model predictive control (MPC) in these settings, respecting timing constraints is achieved by limiting the number of…
The Drude-Smith model has been used extensively in fitting the THz conductivities of nanomaterials with carrier confinement on the mesoscopic scale. Here, we show that the conventional 'backscattering' explanation for the suppression of…