Non-Uniform Automata Over Groups

A Fractal Non-Contracting Class of Automata Groups

UNIFORM AND SEMI-UNIFORM TOPOLOGY ON GENERAL FUZZY AUTOMATA

In this paper, we dene the concepts of compatibility between twofuzzy subsets on Q, the set of states of a max- min general fuzzy automatonand transitivity in a max-min general fuzzy automaton. We then construct auniform structure on Q, and dene a topology on it. We also dene the conceptof semi-uniform structures on a nonempty set X and construct a semi-uniformstructure on the set of states of ...

Post-surjectivity and balancedness of cellular automata over groups

We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every preimage of one is asymptotic to a preimage of the other. The well known dual concept is pre-injectivity: a cellular automaton is pre-injective if distinct asymptotic configurations have distinct images. We prove that pre-injecti...

Non-Uniform Cellular Automata a Review Non-Uniform Cellular Automata a Review

This tutorial intends to present an introduction to non-uniform cellular automata (CA). The difference between uniform cellular automata and non-uniform ones is that in uniform CA all cells share the same rule, or set of rules, in non-uniform CA this is not true, every cell can have a different sets of rules or even no rule at all. We will see here that this single difference increases the powe...

A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group

The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, there are some classes of automata that do not contain such examples. For instance, all infinite Burnside automaton groups in the literature are generated by non reversible Mealy automata and it was recently shown that 2-state invertible-reversible Mealy automata cannot generate infinit...