Related papers: Post-critically finite self-similar groups

Holt and R\"over proved that finitely generated bounded automata groups have indexed co-word problem. Here we sharpen this result to show they are in fact co-ET0L.

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…

We introduce a new class of semigroups arising from a restricted class of asynchronous automata. We call these semigroups "expanding automaton semigroups." We show that the class of synchronous automaton semigroups is strictly contained in…

This paper is a survey of extensions to finite automata theory to model real-time systems as well as systems exhibiting mixed discrete-continuous behavior. Real-time systems maintain a continuous and timely interaction with the environment,…

A quasi-automatic semigroup is a finitely generated semigroup with a rational set of representatives such that the graph of right multiplication by any generator is a rational relation. A asynchronously automatic semigroup is a…

We present a theory of automata with boundary for designing, modelling and analysing distributed systems. Notions of behaviour, design and simulation appropriate to the theory are defined. The problem of model checking for deadlock…

Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…

A class of additive cellular automata (ACA) on a finite group is defined by an index-group $\m g$ and a finite field $\m F_p$ for a prime modulus $p$ \cite{Bul_arch_1}. This paper deals mainly with ACA on infinite commutative groups and…

This paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we characterize the associated semigroup, proving that it is…

We show, that groups, defined by wide class of automata, including all polynomial ones, act on the set of infinite words not paradoxical

We give various characterizations of the covering dimension of the limit space of a contracting self-similar group. In particular, we show that it is equal to the minimal dimension of a contracting affine model, to the asymptotic dimension…

We add to the classification of groups generated by 3-state automata over a 2 letter alphabet given by Bondarenko et al., by showing that a number of the groups in the classification are non-contracting. We show that the criterion we use to…

Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…

Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…

We consider temporal logic verification of (possibly nonlinear) dynamical systems evolving over continuous state spaces. Our approach combines automata-based verification and the use of so-called barrier certificates. Automata-based…

Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups…

Morphic sequences form a natural class of infinite sequences, extending the well-studied class of automatic sequences. Where automatic sequences are known to have several equivalent characterizations and the class of automatic sequences is…

We have recently introduced the two new computing models of self-similar cellular automata and self-similar Petri nets. Self-similar automata result from a progressive, infinite tessellation of space and time. Self-similar Petri nets…

This paper describes a construction of supermartingales realized as automatic functions. A capital of supermartingales is represented using automatic capital groups~(ACG). Properties of these automatic supermartingales are then studied.…

We continue the study of non-invertible topological dynamical systems with expanding behavior. We introduce the class of {\em finite type} systems which are characterized by the condition that, up to rescaling and uniformly bounded…