4 papers
Nonstationary Markov Partitions and Multidimensional Continued Fraction Algorithms
Pierre Arnoux, Valérie Berthé, Milton Minervino +2
It is well known from results of Sina\uı and Bowen that a hyperbolic toral automorphism admits a Markov partition. Our aim is to generalize this concept to the nonstationary case,…
Multidimensional statistics for finite orbits of generalised continued fractions
Valérie Berthé, Stephen Cantrell, Jungwon Lee +1
We statistically compare the relationships between frequencies of digits in continued fraction expansions of typical rational points in the unit interval and higher dimensional gen…
Automata on -adic words
Valérie Berthé, Toghrul Karimov, Mihir Vahanwala
A fundamental question in logic and verification is the following: for which unary predicates is the monadic second-order theory of $\langle \mathbb{N}; <, P_1,…
Density of rational languages under shift invariant measures
Valérie Berthé, Herman Goulet-Ouellet, Dominique Perrin
We study density of rational languages under shift invariant probability measures on spaces of two-sided infinite words, which generalizes the classical notion of density studied i…