Based on a group theoretical setting a sort of discrete dynamical system is constructed and applied to a combinatorial dynamical system defined on the set of certain Bethe ansatz related objects known as the rigged configurations. This system is then used to study a one-dimensional periodic cellular automaton related to discrete Toda lattice. It is shown for the first time that the level set of...

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...

Traditional Fuzzy Automata are not sufficient to model complex real life applications such as biomedical systems where the inputs can be in terms of Fuzzy. Watson Crick Finite Automaton, which works on Double Stranded tapes was introduced a computational analyze DNA molecule for purpose. The concept Fuzziness and studied theory Automaton. thought an effective computing with problems having inco...

We construct a bireversible self-dual automaton with 3 states over an alphabet with 3 letters which generates the lamplighter group Z3 ≀ Z. 2010 Mathematics Subject Classification: 20F65, 20M35

Suppose τ is a cellular automaton over an amenable group and a finite alphabet. Celebrated Garden of Eden theorem states, that pre-injectivity of τ is equivalent to non-existence of Garden of Eden configuration. In this paper we will prove, that imposing some mild restrictions , we could add another equivalent assertion: non-existence of Garden of Eden configuration is equivalent to preservatio...

Let (AZ, F ) be a bipermutative algebraic cellular automaton. We present conditions which force a probability measure which is invariant for the N×Z-action of F and the shift map σ to be the Haar measure on Σ, a closed shift-invariant subgroup of the Abelian compact group AZ. This generalizes simultaneously results of B. Host, A. Maass and S. Mart́ınez [7] and M. Pivato [14]. This result is appl...

We regard internal states of an automaton as emotional states of an individual, its outputs as its actions towards another individual, and a parameter aaecting its state transition as a personal trait. We therefore propose a representation of an individual with emotional states and a certain personality, by a stochastic automaton and a model of a group in which each individual begins conversati...

A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. We say that a sweeping automaton is degenerate if the automaton has no left-moving transitions. We show that for each positive integer n, there is a nondeterministic finite automaton An over a two-letter alphabet such that An has n states, whereas the smallest equivalent nondegenerate swee...