Size-varying reversible causal graph dynamics

TL;DR

This paper explores the possibility of size-varying reversible dynamics in networks, demonstrating reversible local node creation and destruction under relaxed conditions, relevant to reversible computing and quantum gravity models.

Contribution

It introduces three relaxed settings allowing reversible local node creation/destruction and proves their equivalence, advancing understanding of reversible graph dynamics.

Findings

Reversible local node creation/destruction is possible under relaxed conditions.

Three different relaxed settings are shown to be equivalent.

The work connects reversible graph dynamics to quantum gravity models.

Abstract

Consider a network that evolves according to a reversible, nearest neighbours dynamics. Is the dynamics allowed to vary the size of the network? On the one hand it seems that, being the principal carriers of information, nodes cannot be destroyed without jeopardising bijectivity. On the other hand, there are plenty of bijective functions from the set of graphs to the set of graphs that are non-vertex-preserving. The question has been settled negatively -- for three different reasons. Yet, in this paper we do obtain reversible local node creation/destruction -- in three relaxed settings, whose equivalence we prove for robustness. We motivate our work both by theoretical computer science considerations (reversible computing, cellular automata extensions) and theoretical physics concerns (basic formalisms towards discrete quantum gravity).