Intrinsic Universality of Causal Graph Dynamics

TL;DR

This paper introduces a family of intrinsically universal causal graph dynamics that can simulate various instances, capturing key physical symmetries like causality and homogeneity in graph transformations.

Contribution

It constructs a set of universal causal graph dynamics capable of simulating other instances while maintaining their structural properties.

Findings

Constructed a family of intrinsically universal causal graph dynamics

Demonstrated the ability to simulate a subset of instances

Preserved structure and symmetries during simulation

Abstract

Causal graph dynamics are transformations over graphs that capture two important symmetries of physics, namely causality and homogeneity. They can be equivalently defined as continuous and translation invariant transformations or functions induced by a local rule applied simultaneously on every vertex of the graph. Intrinsic universality is the ability of an instance of a model to simulate every other instance of the model while preserving the structure of the computation at every step of the simulation. In this work we present the construction of a family of intrinsically universal instances of causal graphs dynamics, each instance being able to simulate a subset of instances.