Consider a graph having quantum systems lying at each node. Suppose that the whole thing
evolves in discrete time steps, according to a global, unitary causal operator. By causal we …

In this paper, we consider Global Graph Transformations where all occurrences of a set of
predefined local rules are applied altogether synchronously so that each part of the original …

It is well-known that cellular automata can be characterized as the set of translation-invariant
continuous functions over a compact metric space; this point of view makes it easy to extend …

Cayley graphs have a number of useful features: the ability to graphically represent finitely
generated group elements and their relations; to name all vertices relative to a point; and the …

Some models of computation have a notion of underlying space. In this thesis, we study the
way in which information flows over this space in the course of computation, with the aim of …

Based on Gandy's principles for models of computation we give category-theoretic axioms
describing locally deterministic updates to finite objects. Rather than fixing a particular …

We extend Cellular Automata to time-varying discrete geometries. In other words we
formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves …