Reversible graph rewriting modulo an equality theory

Develop a rigorous theory of space-time reversible graph rewriting modulo a graph-name equality theory—potentially inspired by discrete Lorentz transformations—so as to eliminate non-finitary steps and formalize rewriting up to equality.

Background

The time-dilation example introduced by the authors involves non-finitary steps. They suggest that equipping graphs with a suitable equality theory, motivated by discrete versions of Lorentz transformations, could avoid this issue.

To make such an approach fully rigorous, a general framework for reversible graph rewriting modulo equality (analogous to rewriting modulo in term-rewriting systems) is needed, enabling precise handling of equivalence classes of names and patterns during rewriting.