This is an introductory survey of the emerging theory of two new classes of (discrete,
countable) groups, called hyperlinear and sofic groups. They can be characterized as …

Analogy is one of the most effective techniques of human reasoning: When we face new
problems, we compare them with simpler and already known ones, in the attempt to use …

For non-uniform cellular automata (NUCA) over an arbitrary universe with multiple local
transition rules, we introduce and investigate fundamental dynamical properties such as …

For linear nonuniform cellular automata (NUCA) which are local perturbations of linear CA
over a group universe G and a finite-dimensional vector space alphabet V over an arbitrary …

Let G be a group. Let X be a connected algebraic group over an algebraically closed field K.
Denote by A= X (K) the set of K-points of X. We study a class of endomorphisms of pro …

We give a definition of weakly sofic groups (w-sofic groups). Our definition is a rather natural
extension of the definition of sofic groups where instead of the Hamming metric on …

Let $ G $ be a group and let $ k $ be a field. Kaplansky's direct finiteness conjecture states
that every one-sided unit of the group ring $ k [G] $ must be a two-sided unit. In this paper …

The Garden of Eden theorem for linear cellular automata Page 1 Ergod. Th. & Dynam. Sys. (2006),
26, 53–68 c 2006 Cambridge University Press doi:10.1017/S0143385705000520 Printed in …

We establish generalizations of the well-known surjunctivity theorem of Gromov and Weiss
as well as the dual-surjunctivity theorem of Capobianco, Kari and Taati for cellular automata …

In this paper, we introduce the classes of weakly surjunctive and linearly surjunctive groups
which include all sofic groups and more generally all surjunctive groups. We investigate …