相关论文: Automatic groups, subgroups and cosets
We consider the problem of determining the existence of a sequence of matrices driving a discrete-time consensus system to consensus. We transform this problem into one of the existence of a product of the transition (stochastic) matrices…
We explore a natural class of semigroups that have word problem decidable by finite state automata. Among the main results are invariance of this property under change of generators, invariance under basic algebraic constructions and…
Coset incidence geometries, introduced by Jacques Tits, provide a versatile framework for studying the interplay between group theory and geometry. In this article, we build upon that idea by extending classical group-theoretic…
In this article we develop a notion of soficity for actions of countable groups on sets. We show two equivalent perspectives, several natural properties and examples. Notable examples include arbitrary actions of both amenable groups and…
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
We study automatic sequences and automatic systems generated by general constant length (nonprimitive) substitutions. While an automatic system is typically uncountable, the set of automatic sequences is countable, implying that most…
In this paper, we formalize precisely the sense in which the application of cellular automaton to partial configuration is a natural extension of its local transition function through the categorical notion of Kan extension. In fact, the…
The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations…
The axioms of iteration theories, or iteration categories, capture the equational properties of fixed point operations in several computationally significant categories. Iteration categories may be axiomatized by the Conway identities and…
For finitely generated subgroups $H$ of a free group $F_m$ of finite rank $m$, we study the language $L_H$ of reduced words that represent $H$ which is a regular language. Using the (extended) core of Schreier graph of $H$, we construct the…
For an arbitrary group $G$ and arbitrary set $A$, we define a monoid structure on the set of all uniformly continuous functions $A^G\to A$ and then we show that it is naturally isomorphic to the monoid of cellular automata $\mathrm{CA}(G,…
We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and that any self-similar action by bounded automata is…
We introduce graphical complexes of groups, which can be thought of as a generalisation of Coxeter systems with 1-dimensional nerves. We show that these complexes are strictly developable, and we equip the resulting Basic Construction with…
Symmetric cohomology of groups, defined by M. Staic in [2], is similar to the way one defines the cyclic cohomology for algebras. We show that there is a well-defined restriction, conjugation and transfer map in symmetric cohomology, which…
For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length $n$. When this complexity grows exponentially, the automorphism group has been shown to…
We study the connection between small-overlap conditions and automaticity of semigroups. We restrict the discussion to conditions that imply embeddability and under which each relation decomposes into at least seven pieces. For these…
The celebrated Stallings' decomposition theorem states that the splitting of a finite index subgroup $H$ of a finitely generated group $G$ as an amalgamated free product or an HNN-extension over a finite group implies the same for $G$. We…
For profinite branch groups, we first demonstrate the equivalence of the Bergman property, uncountable cofinality, Cayley boundedness, the countable index property, and the condition that every non-trivial normal subgroup is open; compact…
We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific…