We study one-sided substitution subshifts, and how they can be respresented using Bratteli-Vershik systems. In particular we focus on minimal recognizable substitutions such that the generated one-sided substitution subshift contains only one non-shift-invertible element, and we call these substitutions quasi-invertible. We characterise these substitutions, and show that if the substitution is ...

Abstract The general integer mapping theory of invertible linear transforms is considered in this paper. Two terms of integer factor and elementary triangular matrix are introduced. We prove that there exists an integer implementation if a linear transform is invertible and in finite dimensional space. The integer implementation of an invertible linear transform has several advantages such as (...

In the study of hereditary Noetherian rings, it is clear that hereditary Noetherian prime rings will play a central role (see, for example, [12]). Here we study the (two-sided) ideals of an hereditary Xoetherian prime ring and, as a consequence, ascertain the structure of factor rings and torsion modules. The torsion theory represents a generalization of similar results about Dedekind prime rin...

A square matrix is said to be alternating-clean if it is the sum of an alternating matrix and an invertible matrix. In this paper, we determine all alternating-clean matrices over any division ring K. If K is not commutative, all matrices are alternating-clean, with the exception of the 1× 1 zero matrix. If K is commutative, all matrices are alternating-clean, with the exception of odd-size alt...

Let U(n, q) be the group consisting of those invertible matrices A = (ai,j)1≤i,j≤n whose inverse is the conjugate transpose with respect to the involution c 7→ c of the finite field Fq2 . In other words, the i, j’th entry of A is aqj,i. Let μn = 1 |U(n,q)| ∑ A∈U(n,q) Order(A) be the average of the orders of the elements in this finite group. We prove the following conjecture of Fulman: for any ...

In this paper the notion of a quadratic automaton transformation is defined and studied. The automata considered transform infinite input sequences of elements from a finite commutative ring with identity to infinite output sequences. Results extending the linear automaton transformation theory of 4. Nerode are derived and two distinct approaches to machine realization arise depending upon whet...

We study iterated transductions defined by a class of invertible transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show that iterated transductions are rational for a subclass of our automata.

In cryptosystem theory, it is well-known that a logical mapping that returns the same value that was used as its argument can be inverted with a zero failure probability in linear time. In this paper, however, I show that such a mapping, while trivially assigning a logical state to itself, comes up against an impassable entropy wall such that its computational path is undone inside the threshol...

In this paper we introduce the notion of invertible dynamic system, we indicate a very general method to determine the inverse of such a system and we give evidence of the numerous applications of the subclass of dynamic systems defined by this notion. Key-Words: Invertible dynamic system, the inverse of a dynamic system, Lagrange interpolation polynomial.

The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, there are some classes of automata that do not contain such examples. For instance, all infinite Burnside automaton groups in the literature are generated by non reversible Mealy automata and it was recently shown that 2-state invertible-reversible Mealy automata cannot generate infinit...