We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we prove that the context-free language L1 ∗ = {ab : n ≥ 1}∗ can not be recognized by any rational monoid automaton over a finitely generated permutable monoid. We show that the class of la...

ventricular fibrillation is the cause of the most sudden deaths. the recent findings have clearly proved the correlation between the slope of restitution curve with ventricular fibrillation. cellular automata is a powerful tool for simulating complex phenomena in a simple language. in this paper, a simple model is proposed for the simulation of the property of restitution in a single cardiac ce...

We construct the representations of Cayley graphs of wreath products using finite automata, pushdown automata and nested stack automata. These representations are in accordance with the notion of Cayley automatic groups introduced by Kharlampovich, Khoussainov and Miasnikov and its extensions introduced by Elder and Taback. We obtain the upper and lower bounds for a length of an element of a wr...

We study automaton groups without singular points, that is, points in the boundary for which the map that associates to each point its stabilizer, is not continuous. This is motivated by the problem of finding examples of infinite bireversible automaton groups with all trivial stabilizers in the boundary, raised by Grigorchuk and Savchuk. We show that, in general, the set of singular points has...

This paper introduces and discusses a modification of pushdown automata. This modification is based on two-sided pushdowns into which symbols are pushed from both ends. These pushdowns are defined over free groups, not free monoids, and they can be shortened only by the standard group reduction. We demonstrate that these automata characterize the family of recursively enumerable languages even ...

We study two-way tree automata modulo equational theories. We deal with the theories of Abelian groups (ACUM ), idempotent commutative monoids (ACUI), and the theory of exclusive-or (ACUX), as well as some variants including the theory of commutative monoids (ACU ). We show that the one-way automata for all these theories are closed under union and intersection, and emptiness is decidable. For ...

We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image 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-injec...