arXiv subjects

Benjamin Robinson

Publications and source records attributed to Benjamin Robinson.

4 recordsLinked to original sources

arXiv2026

Branching Out: Existential External Choice in Effpi

Effpi is a framework for writing strongly-typed message-passing programs in Scala, where the compiler enforces the conformance of process implementations to specified protocol types. A compiler plugin is provided to verify properties of protocols, such as deadlock-freedom and liveness, by encoding the behavioural types into a variant of CCS. To address limitations in the expressiveness of the existing toolkit, we extend Effpi with external choice by introducing a branching operation. Upon accepting a message via a branch, protocols enforce a continuation which depends on the label (type) of the received message. We equip the branching operation with the ability to accept messages over more than one channel. Additionally, we introduce a "catch timeout" operation to allow processes to gracefully handle a lack of incoming messages. The enhanced expressiveness of Effpi is demonstrated through a number of examples, including an implementation of the Raft consensus algorithm.

cs.PL↗

arXiv2020

Positive operator-valued measures and densely-defined operator-valued frames

In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the purpose of computing measurement probabilities. Frames and their most common generalizations can be seen to give rise to POVMs, but does every reasonable POVM arise from a type of frame? In this paper we answer this question using a Radon-Nikodym-type result.

math.FA↗

arXiv2019

Non-Asymptotic Connectivity of Random Graphs and Their Unions

Graph-theoretic methods have seen wide use throughout the literature on multi-agent control and optimization. When communications are intermittent and unpredictable, such networks have been modeled using random communication graphs. When graphs are time-varying, it is common to assume that their unions are connected over time, yet, to the best of our knowledge, there are not results that determine the number of finite-size random graphs needed to attain a connected union. Therefore, this paper bounds the probability that individual random graphs are connected and bounds the same probability for connectedness of unions of random graphs. The random graph model used is a generalization of the classic Erdos-Renyi model which allows some edges never to appear. Numerical results are presented to illustrate the analytical developments made.

math.OC↗

arXiv2014

Operator-Valued Frames for the Heisenberg Group

A classical result of Duffin and Schaeffer gives conditions under which a discrete collection of characters on $\mathbb{R}$, restricted to $E = (-1/2, 1/2)$, forms a Hilbert-space frame for $L^2(E)$. For the case of characters with period one, this is just the Poisson Summation Formula. Duffin and Schaeffer show that perturbations preserve the frame condition in this case. This paper gives analogous results for the real Heisenberg group $H_n$, where frames are replaced by operator-valued frames. The Selberg Trace Formula is used to show that perturbations of the orthogonal case continue to behave as operator-valued frames. This technique enables the construction of decompositions of elements of $L^2(E)$ for suitable subsets $E$ of $H_n$ in terms of representations of $H_n$.

math.RT↗