Related papers: Complete Boolean Algebra for Memristive and Spintr…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
Memristors are promising next-generation memory candidates that are nonvolatile, possess low power requirements and are capable of nanoscale fabrication. In this article we physically realise and describe the use of organic memristors in…
From the motivation of algebraic attacks to stream and block ciphers([1,2,7,13,14,15]), the concept of {\em algebraic immunity} (AI) was introduced in [21] and studied in [3,5,10,11,17,18,19,20,21]. High algebraic immunity is a necessary…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
Analog IC design is a bottleneck due to its reliance on experience and inefficient simulations, as traditional formulas fail in advanced nodes. Applying Large Language Models (LLMs) directly to this problem risks mere "guessing" without…
Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called {\em enzyme based logic}) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic…
We present a new circuit for non-Boolean recognition of binary images. Employing all-spin logic (ASL) devices, we design logic comparators and non-Boolean decision blocks for compact and efficient computation. By manipulation of fan-in…
Monolithic three-dimensional integration of memory and logic circuits could dramatically improve performance and energy efficiency of computing systems. Some conventional and emerging memories are suitable for vertical integration,…
These notes present a compact and self-contained approach to iterated forcing with a particular emphasis on semiproper forcing. We tried to make our presentation accessible to any scholar who has some familiarity with forcing and boolean…
An Ising model is defined by a quadratic objective function known as the Hamiltonian, composed of spin variables that can take values of either $-1$ or $+1$. The goal is to assign spin values to these variables in a way that minimizes the…
Decomposition of any Boolean Function BF_n of n binary inputs into an optimal inverter coupled network of Symmetric Boolean functions SF_k (k \leq n) is described. Each SF component is implemented by Threshold Logic Cells, forming a…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
Analog in-memory computing (AIMC) is a promising compute paradigm to improve speed and power efficiency of neural network inference beyond the limits of conventional von Neumann-based architectures. However, AIMC introduces fundamental…
An involutive Stone algebra (IS-algebra) is a structure that is simultaneously a De Morgan algebra and a Stone algebra (i.e. a pseudo-complemented distributive lattice satisfying the well-known Stone identity ~xv~~x=1). IS-algebras have…
The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…
Memcomputing logic gates generalize the traditional Boolean logic gates for operation in the reverse direction. According to the literature, this functionality enables the efficient solution of computationally-intensive problems including…
Bayesian Optimal Experimental Design (BOED) provides a rigorous framework for decision-making tasks in which data acquisition is often the critical bottleneck, especially in resource-constrained settings. Traditionally, BOED typically…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
Dense linear algebra libraries, such as BLAS and LAPACK, provide a relevant collection of numerical tools for many scientific and engineering applications. While there exist high performance implementations of the BLAS (and LAPACK)…
Boolean functions and binary arithmetic operations are central to standard computing paradigms. Accordingly, many advances in computing have focused upon how to make these operations more efficient as well as exploring what they can…