73 citations · 200 across the 36 of their papers we have counts for
4 papers · 1 filter
Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types
Xerxes D. Arsiwalla, Jonathan Gorard
How do spaces emerge from pregeometric discrete building blocks governed by computational rules? To address this, we investigate non-deterministic rewriting systems (multiway syste…
Fast Automated Reasoning over String Diagrams using Multiway Causal Structure
Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla
We introduce an intuitive algorithmic methodology for enacting automated rewriting of string diagrams within a general double-pushout (DPO) framework, in which the sequence of rewr…
Homotopies in Multiway (Non-Deterministic) Rewriting Systems as -Fold Categories
Xerxes D. Arsiwalla, Jonathan Gorard, Hatem Elshatlawy
We investigate algebraic and compositional properties of abstract multiway rewriting systems, which are archetypical structures underlying the formalism of the Wolfram model. We de…
ZX-Calculus and Extended Wolfram Model Systems II: Fast Diagrammatic Reasoning with an Application to Quantum Circuit Simplification
Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla
This article presents a novel algorithmic methodology for performing automated diagrammatic deductions over combinatorial structures, using a combination of modified equational the…