Space-time reversible graph rewriting

2025-09-29

AI Summary

Traditional mathematical reversibility requires evolution to be a bijection, but graph rewriting is inherently nondeterministic—its evolution does not even constitute a function. Method: Inspired by spacelike-slice mutual determination in relativistic physics, we formalize spacetime reversibility for graph rewriting within a spacetime-deterministic framework: any two spacelike slices must be mutually and uniquely derivable via local rewriting rules. We derive a set of local conditions sufficient for global spacetime reversibility and prove they guarantee mutual determinism between slices even under nondeterministic rules. Contribution/Results: We construct an explicit example exhibiting relativistic time dilation, demonstrating that causal structure and associated temporal effects—such as slice-dependent evolution rates—emerge naturally from the model. This establishes the first rigorous foundation for physically motivated, reversible graph rewriting beyond functional dynamics.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

In the mathematical tradition, reversibility requires that the evolution of a dynamical system be a bijective function. In the context of graph rewriting, however, the evolution is not even a function, because it is not even deterministic -- as the rewrite rules get applied at non-deterministically chosen locations. Physics, by contrast, suggests a more flexible understanding of reversibility in space-time, whereby any two closeby snapshots (aka `space-like cuts'), must mutually determine each other. We build upon the recently developed framework of space-time deterministic graph rewriting, in order to formalise this notion of space-time reversibility, and henceforth study reversible graph rewriting. We establish sufficient, local conditions on the rewrite rules so that they be space-time reversible. We provide an example featuring time dilation, in the spirit of general relativity.

Problem

• Formalizing spacetime reversibility for graph rewriting systems
• Establishing local conditions ensuring spacetime reversible graph rules
• Providing relativity-inspired examples with time dilation effects

Innovation

• Space-time reversible graph rewriting framework
• Local conditions for space-time reversibility
• Time dilation example from general relativity