The concept of self-similar automata over a changing alphabet and lamplighter groups generated by such automata

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.

Cross-wired lamplighter groups and linearity of automata groups

We consider the two generalizations of lamplighter groups: automata groups generated by Cayley machines and cross-wired lamplighter groups. For a finite step two nilpotent group with central squares, we study its associated Cayley machine and give a presentation of the corresponding automata group. We show the automata group is a crosswired lamplighter group and does not embed in the wreath pro...

Groups and Semigroups Generated by Automata

In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, self-similar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups " expanding automaton semigroups ". W...

Unambiguous Finite Automata over a Unary Alphabet

Nondeterministic finite automata (NFA) with at most one accepting computation on every input string are known as unambiguous finite automata (UFA). This paper considers UFAs over a one-letter alphabet, and determines the exact number of states in DFAs needed to represent unary languages recognized by n-state UFAs in terms of a new number-theoretic function g̃. The growth rate of g̃(n), and theref...

Investigations on Automata and Languages over a Unary Alphabet