Size-varying reversible causal graph dynamics

2018-05-25

AI Summary

Conventional wisdom holds that reversible graph dynamics must preserve the number of nodes, precluding node creation or deletion while maintaining reversibility. Method: This paper challenges this paradigm by introducing three mutually equivalent relaxed frameworks—grounded in reversible computation, extended cellular automata, and bijective graph rewriting—that jointly enforce global bijectivity and local causality while permitting reversible node creation and destruction. Contribution/Results: We formally prove the equivalence of these frameworks, thereby establishing the first causal graph dynamics model that is both size-variable and time-reversible. This work refutes the long-standing assumption that reversibility necessitates node conservation, offering a novel paradigm for discrete spacetime modeling. It bridges a critical gap between theoretical computer science—particularly models of reversible computation—and formal approaches to quantum gravity, where dynamical causal structure and background independence are essential.

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).

Problem

• Study reversible dynamics altering network size
• Explore node creation/destruction preserving reversibility
• Link theory to computing and quantum gravity

Innovation

• Reversible local node creation/destruction dynamics
• Relaxed settings for robust equivalence
• Motivated by reversible computing and quantum gravity