Year: 2026
Type: preprint
Abstract: We introduce causal graph rewriting, a model of computation in which local rules are applied on directed acyclic graphs in an asynchronous manner. The non-determinism arising from asynchrony is disciplined by the oriented edges, which must be understood as both computational dependencies and locality constraints---and are themselves subject to the rewriting. We illustrate the model through two examples: a particle system, and a time-dilation example---reminiscent of general relativity. We study the well-definedness and properties of induced subgraphs and graph composition, which isolate and recombine the region affected by a rewrite. We then study locality with respect to these constructions, showing how a local rewrite preserves positions, borders, and context. Our main result concerns sequential composition: locality extends from single rule applications to arbitrary valid sequences, as any local rule is automatically $*$-local and $*$-extensive. We also formalise and prove the simulation of any one-dimensional cellular automaton.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1693829329, Etude de la pile quantique : Algorithmes, modèles de calcul et simulation pour l’informatique quantique, Initiative Nationale Hybride HPC Quantique – R&D et Support des communautés, Initiative Nationale Hybride HPC Quantique - Acquisition, Taming Quantum Causality, WithOut SpaceTime (WOST), G7080048889
OpenAlex ID: W7214088731