10 citations · 17 across the 7 of their papers we have counts for
8 papers
Cellular Automata on Group Sets
Simon Wacker
We introduce and study cellular automata whose cell spaces are left-homogeneous spaces. Examples of left-homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spa…
Signal Machine And Cellular Automaton Time-Optimal Quasi-Solutions Of The Firing Squad/Mob Synchronisation Problem On Connected Graphs
Simon Wacker
We construct a time-optimal quasi-solution of the firing mob synchronisation problem over finite, connected, and undirected multigraphs whose maximum degrees are uniformly bounded…
The Moore and the Myhill Property For Strongly Irreducible Subshifts Of Finite Type Over Group Sets
Simon Wacker
We prove the Moore and the Myhill property for strongly irreducible subshifts over right amenable and finitely right generated left homogeneous spaces with finite stabilisers. Both…
Right Amenability And Growth Of Finitely Right Generated Left Group Sets
Simon Wacker
We introduce right generating sets, Cayley graphs, growth functions, types and rates, and isoperimetric constants for left homogeneous spaces equipped with coordinate systems; char…
Right Amenable Left Group Sets and the Tarski-Følner Theorem
Simon Wacker
We introduce right amenability, right Følner nets, and right paradoxical decompositions for left homogeneous spaces and prove the Tarski-Følner theorem for left homogeneous spaces…
The Garden of Eden Theorem for Cellular Automata on Group Sets
Simon Wacker
We prove the Garden of Eden theorem for cellular automata with finite set of states and finite neighbourhood on right amenable left homogeneous spaces with finite stabilisers. It s…
Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon Theorem
Simon Wacker
We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of…
Phase Space Invertible Asynchronous Cellular Automata
Simon Wacker, Thomas Worsch
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first dis…