Related papers: Delay-Optimum Adder Circuits with Linear Size
A notorious open question in circuit complexity is whether Boolean operations of arbitrary arity can efficiently be expressed using modular counting gates only. H{\aa}stad's celebrated switching lemma yields exponential lower bounds for the…
The best known size lower bounds against unrestricted circuits have remained around $3n$ for several decades. Moreover, the only known technique for proving lower bounds in this model, gate elimination, is inherently limited to proving…
Let $s$ be a finite sequence over a field of length $n$. It is well-known that if $s$ satisfies a linear recurrence of order $d$ with non-zero constant term, then the reverse of $s$ also satisfies a recurrence of order $d$ (with…
We propose an algorithm with expected complexity of $\bigO(n\log n)$ arithmetic operations to solve a special shortest vector problem arising in computer-and-forward design, where $n$ is the dimension of the channel vector. This algorithm…
In this work faster Baugh-Wooley multiplication has been achieved by using a combination of two design techniques: partition of the partial products into two parts for independent parallel column compression and acceleration of the final…
We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of…
We give an algorithm for finding network encoding and decoding equations for error-free multicasting networks with multiple sources and sinks. The algorithm given is efficient (polynomial complexity) and works on any kind of network…
We design two incremental algorithms for computing an inclusion-minimal completion of an arbitrary graph into a cograph. The first one is able to do so while providing an additional property which is crucial in practice to obtain…
Accelerating the solution of linear systems of equations is critical due to their central role in numerous applications, such as numerical simulations, data analytics, and machine learning. This paper presents an analog solver circuit…
We prove that for an $L$-layer fully-connected linear neural network, if the width of every hidden layer is $\tilde\Omega (L \cdot r \cdot d_{\mathrm{out}} \cdot \kappa^3 )$, where $r$ and $\kappa$ are the rank and the condition number of…
Flexibility and customization are key strengths of Field-Programmable Gate Arrays (FPGAs) when compared to other computing devices. For instance, FPGAs can efficiently implement arbitrary-precision arithmetic operations, and can perform…
Given the stringent requirements of energy efficiency for Internet-of-Things edge devices, approximate multipliers, as a basic component of many processors and accelerators, have been constantly proposed and studied for decades, especially…
The MUX implementation of ternary half adders and full adders using predecessor and successor functions lead to the most efficient efficient implementation using the smallest transistor count. These designs are compared with the binary…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
We construct $n$-node graphs on which any $O(n)$-size spanner has additive error at least $+\Omega(n^{3/17})$, improving on the previous best lower bound of $\Omega(n^{1/7})$ [Bodwin-Hoppenworth FOCS '22]. Our construction completes the…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
One of the main goals in quantum circuit optimisation is to reduce the number of ancillary qubits and the depth of computation, to obtain robust computation. However, most of known techniques, based on local rewriting rules, for…
Designing high-performance error-correcting codes at short blocklengths is critical for low-latency communication systems, where decoding is governed by finite-length and graph-structural effects rather than asymptotic properties. This…
The distance profiles of linear block codes can be employed to design variational coding scheme for encoding message with variational length and getting lower decoding error probability by large minimum Hamming distance. %, e.g. the design…
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields…