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Sequential computation is well understood but does not scale well with current technology. Within the next decade, systems will contain large numbers of processors with potentially thousands of processors per chip. Despite this, many…
The worst-case complexity of group-theoretic algorithms has been studied for a long time. Generic-case complexity, or complexity on random inputs, was introduced and studied relatively recently. In this paper, we address the average-case…
Deep neural networks generate and process large volumes of data, posing challenges for low-resource embedded systems. In-memory computing has been demonstrated as an efficient computing infrastructure and shows promise for embedded AI…
In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…
Entropic uncertainty relations are universal quantifiers of fundamental uncertainties of quantum measurements and are widely discussed in the quantum metrology literature. Quantum memory is a phenomenon related to the specific type of…
We are concerned with the complexity reduction of a stochastic system of differential equations governing the dynamics of a neuronal circuit describing a decision-making task. This reduction is based on the slow-fast behavior of the problem…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
We describe a matrix multiplication recognition algorithm for a subset of binary linear context-free rewriting systems (LCFRS) with running time $O(n^{\omega d})$ where $M(m) = O(m^{\omega})$ is the running time for $m \times m$ matrix…
Based on bottom-up assembly of highly variable neural cells units, the nervous system can reach unequalled level of performances with respect to standard materials and devices used in microelectronic. Reproducing these basic concepts in…
Feedback-driven quantum reservoir computing has so far been studied primarily in gate-based architectures, motivating alternative scalable, hardware-friendly physical platforms. Here we investigate a linear-optical quantum reservoir…
We study a mutually enriching connection between response time analysis in real-time systems and the mixing set problem. Thereby generalizing over known results we present a new approach to the computation of response times in…
We consider the problem of solving linear systems of equations arising with limited-memory members of the restricted Broyden class of updates and the symmetric rank-one (SR1) update. In this paper, we propose a new approach based on a…
We establish an improved classical algorithm for solving linear systems in a model analogous to the QRAM that is used by quantum linear solvers. Precisely, for the linear system $A\x = \b$, we show that there is a classical algorithm that…
This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no…
While well-known methods to list the intersections of either a list of segments or a complex polygon aim at achieving optimal time-complexity they often do so at the cost of memory comsumption and complex code. Real-life software…
The solving of least square systems is a useful operation in neurocomputational modeling of learning, pattern matching, and pattern recognition. In these last two cases, the solution must be obtained on-line, thus the time required to solve…
Large transformer models have shown extraordinary success in achieving state-of-the-art results in many natural language processing applications. However, training and deploying these models can be prohibitively costly for long sequences,…
Recently, studying fundamental graph problems in the \emph{Massively Parallel Computation (MPC) framework, inspired by the MapReduce paradigm, has gained a lot of attention. An assumption common to a vast majority of approaches is to allow…