We consider a method for assigning a sofic shift to a (not necessarily nonnegative integer) matrix by associating to it a directed graph with some vertices labelled 1 and the rest 2 (the decomposition of the vertices is arbitrary in applications the choice should be natural). We can detect positive topological entropy for this sofic shift by comparing the characteristic polynomial of the origin...

We study shift spaces associated with a family of transformations generating expansions in base −β, with β > 1. We give a complete characterization when these shift spaces are sofic or even shifts of finite type.

This article is a summary of the plenary lecture that I gave at the 1995 IEEE International Symposium on Information Theory. The lecture was intended to give a concrete and elementary introduction to the subject of symbolic dynamics. From my point of view, symbolic dynamics is the subject of \coding" from one \constrained set" of sequences to another. Of course, there are restrictions on what I...

We study nearest-neighbor shifts of finite type (NNSOFT) on a free group G. We determine when a NNSOFT on G admits a periodic coloring and give an example of a NNSOFT that does not allow a periodic coloring. Then, we find an expression for the entropy of the golden mean shift on G. In doing so, we study a new generalization of Fibonacci numbers and analyze their asymptotics with a one-dimension...

A set P ⊆ {0,1}N may be viewed as a mass problem, i.e., a decision problem with more than one solution. By definition, the solutions of P are the elements of P . A mass problem is said to be solvable if at least one of its solutions is recursive. A mass problem P is said to be Muchnik reducible to a mass problem Q if for each solution of Q there exists a solution of P which is Turing reducible ...

The aim of this paper is to study local configurations issued from discrete rotations. The algorithm of discrete rotations that we consider is the discretized rotation. It simply consists in the composition of a Euclidean rotation with a rounding operation, as studied in [B. Nouvel, E. Rémila, On colorations induced by discrete rotations, in: DGCI, in: LNCS, vol. 2886, 2003, pp. 174–183; B. Nou...

We study the family of the Lozi maps La,b : R2 → R2, La,b(x, y) = (1+y−a|x|, bx), and their strange attractors Λa,b. We introduce the set of kneading sequences for the Lozi map and prove that it determines the symbolic dynamics for that map. We also introduce two other equivalent approaches. 2010 Mathematics Subject Classification: 37B10, 37D45, 37E30, 54H20