Related papers: Recognizability for sequences of morphisms
We investigate questions related to the notion of recognizability of sequences of morphisms, a generalization of Moss{\'e}'s Theorem. We consider the most general class of morphisms including ones with erasable letters. The main result…
We investigate several questions related to the notion of recognizable morphism. The main result is a new proof of Moss\'e's theorem and actually of a generalization to non primitive morphisms due to Berth\'e et al. We actually prove the…
In this work we study $S$-adic shifts generated by sequences of morphisms that are constant-length. We call a sequence of constant-length morphisms torsion-free if any prime divisor of one of the lengths is a divisor of infinitely many of…
In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We prove the decidability of many properties of these morphisms with respect to the…
Moss\'e proved that primitive morphisms are recognizable. In this paper we give a computable upper bound for the constant of recognizability of such a morphism. This bound can be expressed only using the cardinality of the alphabet and the…
We develop a general framework of Euclidean patterns and pattern spaces of translational finite local complexity (FLC), analogues of translational tiling spaces. The notion of a self affine substitution of tilings is extended to both…
Motivated by applications in the theory of numeration systems and recognizable sets of integers, this paper deals with morphic words when erasing morphisms are taken into account. Cobham showed that if an infinite word $w =g(f^\omega(a))$…
An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…
Given a monoid $(M,\varepsilon,\cdot )$ it is shown that a subset $A\subseteq M$ is recognizable in the sense of automata theory if and only if the $\varphi $-rank of $x=x$ is zero in the first-order theory $\operatorname{Th}(M,\varepsilon…
Dendric shifts are defined by combinatorial restrictions of the extensions of the words in their languages. This family generalizes well-known families of shifts such as Sturmian shifts, Arnoux-Rauzy shifts and codings of interval exchange…
We prove equality of the various $p$-adic period morphisms for smooth, not necessarily proper, schemes. We start with showing that the $K$-theoretical uniqueness criterium we had found for proper smooth schemes extends to proper finite…
We prove in an elementary fashion that the image of a commutative monotone $\sigma$-complete $C^*$-algebra under a $\sigma$-normal morphism is again monotone $\sigma$-complete and give an application of this result in spectral theory.
Countable Markov shifts, denoted by $\Sigma_A$ for a 0-1 infinite matrix $A$, are central objects in symbolic dynamics and ergodic theory. R. Exel and M. Laca introduced the corresponding operator algebras, a generalization of the…
Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite…
In this note we prove the following results: $\bullet$ If a finitely presented group $G$ admits a strongly aperiodic SFT, then $G$ has decidable word problem. More generally, for f.g. groups that are not recursively presented, there exists…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
The free monoid $A^*$ on a finite totally ordered alphabet $A$ acts at the left on columns, by Schensted left insertion. This defines a finite monoid, denoted $Styl(A)$ and called the stylic monoid. It is canonically a quotient of the…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
It is known that each word of length $n$ contains at most $n+1$ distinct palindromes. A finite rich word is a word with maximal number of palindromic factors. The definition of palindromic richness can be naturally extended to infinite…
The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…