From Border-Agnosticism to Causal Rewrite Systems

Causal Graph Rewriting was recently introduced as an evolution of Causal Graph Dynamics to allow for a controlled form of asynchronism in these dynamical systems with dynamical graphs. In this context, the notion of borders—akin to dangling edges—has gained increasing importance. In this paper, we re-examine these borders, interpreting them as missing information. This perspective adds structural rigor to the framework, allowing border-agnostic causal graph rewriting to be reformulated as a rewriting system rather than a dynamical system. This shift represents a crucial step toward facilitating the treatment of reversibility.