Related papers: Concurrent Kleene Algebra: Free Model and Complete…
The verification of multithreaded software is still a challenge. This comes mainly from the fact that the number of thread interleavings grows exponentially in the number of threads. The idea that thread interleavings can be studied with a…
Despite the success of fine-tuning pretrained language encoders like BERT for downstream natural language understanding (NLU) tasks, it is still poorly understood how neural networks change after fine-tuning. In this work, we use centered…
The question of whether quantum real-time one-counter automata (rtQ1CAs) can outperform their probabilistic counterparts has been open for more than a decade. We provide an affirmative answer to this question, by demonstrating a…
Concurrent program refinement algebra provides a suitable basis for supporting mechanised reasoning about shared-memory concurrent programs in a compositional manner, for example, it supports the rely/guarantee approach of Jones. The…
In a paper published in Information Processing Letters in 2000, Bouajjani et al. presented an automata-based approach to a number of elementary problems on context-free grammars. This approach is of pedagogical interest since it provides a…
This article provides a primer on the spectral representation of random fields via the Karhunen-Lo\`eve Expansion (KLE). The goal is to bridge the gap between the theoretical foundations of the KLE and its application in computational…
Given an arbitrary infinite 0--1 matrix A having no identically zero rows, we define an algebra OA as the universal C*-algebra generated by partial isometries subject to conditions that generalize, to the infinite case, those introduced by…
The system $\mathsf{Clo}$ is a cyclic, cut-free proof system for the modal $\mu$-calculus. It was introduced by Afshari & Leigh as an intermediate system in their intent to show the completeness of Kozen's axiomatisation for the modal…
The use of Extended Logics to replace ordinary second order definability in Kleene's {\em Ramified Analytical Hierarchy} is investigated. This mirrors a similar investigation of Kennedy, Magidor and V\"a\"an\"anen \cite{KeMaVa2016} where…
The purpose of this paper is to give a self-contained overview of the theory of matrix convex sets and free spectrahedra. We will give new proofs and generalizations of key theorems. However we will also introduce various new concepts and…
This paper considers the problem of canonical-correlation analysis (CCA) (Hotelling, 1936) and, more broadly, the generalized eigenvector problem for a pair of symmetric matrices. These are two fundamental problems in data analysis and…
In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with which to study QCA models. Then we present four different…
For a symmetrizable GCM $C$ and its symmetrizer $D$, Geiss-Leclerc-Schr\"oer [Invent. Math. 209 (2017)] has introduced a generalized preprojective algebra $\Pi$ associated to $C$ and $D$, that contains a class of modules, called locally…
We solve MIT's Linear Algebra 18.06 course and Columbia University's Computational Linear Algebra COMS3251 courses with perfect accuracy by interactive program synthesis. This surprisingly strong result is achieved by turning the course…
We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irredundant covering.
Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical…
An old dream of concurrency theory and programming language semantics has been to uncover the fundamental synchronization mechanisms which regulate situations as different as game semantics for higher-order programs, and Hoare logic for…
This paper is dedicated to enhancing the computational efficiency of traditional parallel-in-time methods for solving stochastic initial-value problems. The standard parareal algorithm often suffers from slow convergence when applied to…
Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string…
Finding overcomplete latent representations of data has applications in data analysis, signal processing, machine learning, theoretical neuroscience and many other fields. In an overcomplete representation, the number of latent features…