A structure is automatic if its domain, functions, and relations are all regular languages.
Using the fact that every automatic structure is decidable, in the literature many decision …

In this paper we introduce the concept of a Cayley graph automatic group (CGA group or
graph automatic group, for short) which generalizes the standard notion of an automatic …

The objective of this survey is to present the ideal theory of monoids, the so-called Green's
relations, and to illustrate the usefulness of this tool for solving automata related questions …

Semiautomatic structures generalise automatic structures in the sense that for some of the
relations and functions in the structure one only requires the derived relations and functions …

We prove that the irreducible affine Coxeter groups are first-order rigid and deduce from this
that they are profinitely rigid in the absolute sense. We then show that the first-order theory of …

The 2022 logic blog has concentrated on the connections of group theory and logic. It
discusses Gardam's 2021 refutation of the Higman/Kaplansky unit conjecture, and its …

Automatic classes are classes of languages for which a finite automaton can decide whether
a given element is in a set given by its index. The present work studies the learnability of …

Tree-automatic linear orders on regular tree languages are studied. It is shown that there is
no tree-automatic scattered linear order, and therefore no tree-automatic well-order, on the …

We construct a FA–presentation ψ: L→ N of the structure (N; S) for which a numerical
characteristic r (n) defined as the maximum number ψ (w) for all strings w∈ L of length less …

We propose a new generalization of Cayley automatic groups, varying the time complexity of
computing multiplication, and language complexity of the normal form representatives. We …