Size-varying reversible causal graph dynamics
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.