Related papers: Automaton (Semi)groups (Basic Concepts)

We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…

We are interested in formulas for the number of elements in certain classes of numerical semigroups

We provide an introduction to Quantum Cellular Automata.

In 2019, V. A. Roman'kov introduced the concept of marginal sets for groups. He developed a theory of marginal sets and demonstrated how these sets can be applied to improve some key exchange schemes. In this paper, we extend his ideas and…

The notion of nearly abelian rational semigroup was introduced by Hinkannen and Martin. In this paper, we have introduced the notion of nearly abelian transcendental semigroup. We have extended the results of nearly abelian rational…

An elementary introduction to the non-perturbative renormalization group is presented mainly in the context of statistical mechanics. No prior knowledge of field theory is necessary. The aim is this article is not to give an extensive…

In this paper we show that a recently published finite automaton stream cipher can be considered as a quasigroup based stream cipher. Some additional properties of the discussed cipher are also given.

We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…

We present an accessible introduction to basic results on groups of intermediate growth.

We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show, with some examples, that representation theory of semigroups is related to usual constructions in…

Since first introduced by John von Neumann, the notion of cellular automaton has grown into a key concept in computer science, physics and theoretical biology. In its classical setting, a cellular automaton is a transformation of the set of…

In this paper we show the way we pass from semigroups (without order) to hypersemigroups. Moreover we show that, exactly as in semigroups, in the results of hypersemigroups based on right (left) ideals, quasi-ideals and bi-ideals, points do…

This paper concerns the general problem of classifying the finite deterministic automata that admit a synchronizing (or reset) word. (For our purposes it is irrelevant if the automata has initial or final states.) Our departure point is the…

This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results…

This paper addresses the torsion problem for a class of automaton semigroups, defined as semigroups of transformations induced by Mealy automata, aka letter-by-letter transducers with the same input and output alphabet. The torsion problem…

This technical description details the design and engineering process of a semi-autonomous robotic partition. This robotic partition prototype was subsequently employed in a longer-term evaluation in-the-wild study conducted by the authors…

We introduce a ring and a field, generated by a semigroup, and we investigate some of their properties.

Motivated by intuitive properties of physical quantities, the notion of a non-anomalous semigroup is formulated. These are totally ordered semigroups where there are no `infinitesimally close' elements. The real numbers are then defined as…

We consider the lattice of subsemigroups of the general linear group over an Artinian ring containing the group of diagonal matrices and show that every such semigroup is actually a group.

Motivated by situations in which the removal of a zero (a.k.a., an absorbing element) from a semigroup yields a subsemigroup with another zero, sets of quasi-zeros (a.k.a., quasi-absorbing elements) are introduced as well as primitive…