Universality of causal graph dynamics

TL;DR

This paper explores the universality of Causal Graph Dynamics, a generalization of Cellular Automata to dynamic graphs, focusing on their ability to simulate other models under causality and homogeneity constraints.

Contribution

It introduces three notions of simulation for Causal Graph Dynamics and defines universality within this framework.

Findings

Defined three notions of simulation for Causal Graph Dynamics

Established conditions for universality in these models

Demonstrated the capacity of Causal Graph Dynamics to simulate other computational models

Abstract

Causal Graph Dynamics generalize Cellular Automata, extending them to bounded degree, time varying graphs. The dynamics rewrite the graph at each time step with respect to two physics-like symmetries: causality (bounded speed of information) and homogeneity (the rewriting acts the same everywhere on the graph, at every time step). Universality is the ability simulating every other instances of another (or the same) model of computation. In this work, we study three different notions of simulation for Causal Graph Dynamics, each of them leading to a definition of universality.