Related papers: The Structure of In-Place Space-Bounded Computatio…

In practice, many machine learning (ML) problems come with constraints, and their applied domains involve distributed sensitive data that cannot be shared with others, e.g., in healthcare. Collaborative learning in such practical scenarios…

Let $F=\{\mathbf{p}_0,\ldots,\mathbf{p}_n\}$ be a collection of points in $\mathbb{R}^d.$ The set $F$ naturally gives rise to a family of iterated function systems consisting of contractions of the form $$S_i(\mathbf{x})=\lambda \mathbf{x}…

We give a quantum logspace algorithm for powering contraction matrices, that is, matrices with spectral norm at most~1. The algorithm gets as an input an arbitrary $n\times n$ contraction matrix $A$, and a parameter $T \leq…

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…

Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…

Catalytic computing concerns space bounded computation which starts with memory full of data that have to be restored by the end of the computation. Lossy catalytic computing, defined by Gupta et al. (2024) and fully characterized by…

For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.

Among the paradigms for parallel and distributed computing, the one popularized with Linda, and based on tuple spaces, is one of the least used, despite the fact of being intuitive, easy to understand and to use. A tuple space is a…

One requirement of maintaining digital information is storage. With the latest advances in the digital world, new emerging media types have required even more storage space to be kept than before. In fact, in many cases it is required to…

In this paper we study the following problem: for a given bounded positive function $f$ on a filtered probability space can we find another function (a multiplier) $m$, $0\le m\le 1$, such that the function $mf$ is not ``too small'' but its…

Federated Learning (FL) is plagued by two key challenges: high communication overhead and performance collapse on heterogeneous (non-IID) data. Analytic FL (AFL) provides a single-round, data distribution invariant solution, but is limited…

We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…

Five simple guidelines are proposed to compute the generating function for the nonnegative integer solutions of a system of linear inequalities. In contrast to other approaches, the emphasis is on deriving recurrences. We show how to use…

We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of…

Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…

First-order model counting (FOMC) is the problem of counting the number of models of a sentence in first-order logic. Since lifted inference techniques rely on reductions to variants of FOMC, the design of scalable methods for FOMC has…

In this paper, we develop a quantified propositional proof systems that corresponds to logarithmic-space reasoning. We begin by defining a class SigmaCNF(2) of quantified formulas that can be evaluated in log space. Then our new proof…

By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…

We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…

In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite…