Some criteria for determining recognizability of a set

Let an be the number of strings of length n in a set A ⊆ ∑*, where ∑ is a finite alphabet. Several criteria for determining that a set is not recognizable by a finite automaton are given, based solely on the sequence {an}. The sequence {an} is also used to define a finitely addititive probability measure on all recognizable sets

On some spectral properties of TanDEM-X interferograms over forested areas

This letter reports about some obervations over rainforest (in Brazil and Indonesia), where the spectra of TanDEM-X interferograms show distinct features, almost a signature, which is explained and modelled in terms of the scattering properties. Supported by comparisons with simulations, the observations exclude any homogeneous, horizontally-layered forest; instead, they are compatible with a model with point scatterers clustered in clouds. Such a model, with high extinction and large gaps that allow significant penetration, is able to explain to a good degree the observations

Some properties of B\"uchi Arithmetics

B\"uchi arithmetics $\mathop{\mathbf{BA}}\nolimits_n$, $n\ge 2$, are extensions of Presburger arithmetic with an unary functional symbol $V_n(x)$ denoting the largest power of $n$ that divides $x$. A rank of a linear order is the minimal number of condensations required to reach a finite order. We show that linear orders of arbitrarily large finite rank can be interpreted in $\mathop{\mathbf{BA}}\nolimits_n$. We also prove that the extension of the axioms of Presburger arithmetic with the inductive definition of $V_n$ does not yield an axiomatization of $\mathop{\mathbf{BA}}\nolimits_n$.Comment: 6 pages. The publication was prepared within the framework of the Academic Fund Program at HSE University (grant 23-00-022

Logics for Unranked Trees: An Overview

Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees

Asymptotic properties of free monoid morphisms

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 $w =g(f^\omega(a))$ is the image of a fixed point of a morphism $f$ under another morphism $g$, then there exist a non-erasing morphism $\sigma$ and a coding $\tau$ such that $w =\tau(\sigma^\omega(b))$. Based on the Perron theorem about asymptotic properties of powers of non-negative matrices, our main contribution is an in-depth study of the growth type of iterated morphisms when one replaces erasing morphisms with non-erasing ones. We also explicitly provide an algorithm computing $\sigma$ and $\tau$ from $f$ and $g$.Comment: 25 page