2024/06/24 by Tomáš Gonda, Gemma De les Coves, Gonda, Tomáš +1 · 1 voice
Computer Science · Psychology · #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Mathematics education #Physics #Psychology #Quantum mechanics #Statistical physics #Theoretical physics #Universality (dynamical systems)
paper · pdf · doi:10.48550/arxiv.2406.16607
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system. Our categorical framework for universality (arXiv:2307.06851) captures these and other examples of universality as instances. In this article, we present an accessible account thereof with a focus on its basic ingredients and ways to use it. Specifically, we show how to identify necessary conditions for universality, compare types of universality within each instance, and establish that universality and negation give rise to unreachability (such as uncomputability).