Automata groups

A Fractal Non-Contracting Class of Automata Groups

Cloud modeling of quasi - order groups on general fuzzy automata

In this paper, first a simplified version of a general fuzzy automaton with a fixed c is defined and then a subepisode of a simplified version of a general fuzzy automaton with a constant c is defined and explained connected and strong connected them, and finally, a model of quasi-order hypergroup on general fuzzy automaton with constant c is presented and the relationships between them are rev...

A Novel Approach for Detecting Relationships in Social Networks Using Cellular Automata Based Graph Coloring

All the social networks can be modeled as a graph, where each roles as vertex and each relationroles as an edge. The graph can be show as G = [V;E], where V is the set of vertices and E is theset of edges. All social networks can be segmented to K groups, where there are members in eachgroup with same features. In each group each person knows other individuals and is in touch ...

Groups and Automata: a Perfect Match

We present a personal perspective, inspired by our own research experience, of the interaction between group theory and automata theory: from Benois’ Theorem to Stallings’ automata, from hyperbolic to automatic groups, not forgetting the exotic automaton groups.

ON SOMEWHAT FUZZY AUTOMATA CONTINUOUS FUNCTIONS IN FUZZY AUTOMATA TOPOLOGICAL SPACES

In this paper, the concepts of somewhat fuzzy automata continuous functions and somewhat fuzzy automata open functions in fuzzy automata topological spaces are introduced and some interesting properties of these functions are studied. In this connection, the concepts of fuzzy automata resolvable spaces and fuzzy automata irresolvable spaces are also introduced and their properties are studied.

On a Class of Automata Groups Generalizing Lamplighter Groups

We study automata groups generated by reset automata. Every lamplighter group Z/nZ wr Z can be generated by such an automaton, and in general these automata groups are similar in nature to lamplighters: they are amenable locally-finite-by-cyclic groups; under mild decidable conditions, the semigroups generated by such automata are free. Parabolic subgroups and fractal properties are considered.