Related papers: Rhythmic generation of infinite trees and language…
We probe the layers in multilingual BERT (mBERT) for phylogenetic and geographic language signals across 100 languages and compute language distances based on the mBERT representations. We 1) employ the language distances to infer and…
This paper deals with various cases of resonance, which is a fundamental concept of science and engineering. Specifically, we study the connections between periodic and unbounded solutions for several classes of equations and systems. In…
In a previous work we introduced slice graphs as a way to specify both infinite languages of directed acyclic graphs (DAGs) and infinite languages of partial orders. Therein we focused on the study of Hasse diagram generators, i.e., slice…
Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process.…
Logical frameworks are successful in modeling proof systems. Recently, CoLF extended the logical framework LF to support higher-order rational terms that enable adequate encoding of circular objects and derivations. In this paper, we…
The present study has two goals relating to the grammar of prosody, understood as the rhythms and melodies of speech. First, an overview is provided of the computable grammatical and phonetic approaches to prosody analysis which use…
Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words…
We study a branching-process random iterated function system (RIFS) defined by a recursive replacement of leaves by finite subtrees at strictly smaller contraction scales. This construction yields a tree-valued, infinite-depth random…
We introduce $L^2_{K,P}$, a monadic second-order language for reasoning about trees which characterizes the strongly Context-Free Languages in the sense that a set of finite trees is definable in $L^2_{K,P}$ iff it is (modulo a projection)…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
In this paper, I discuss two logics for weighted finite structures: first-order logic with summation (FO(SUM)) and its recursive extension IFP(SUM). These logics originate from foundational work by Gr\"adel, Gurevich, and Meer in the 1990s.…
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behaviours of the shattering times, defined as the first instants when all the blocks of…
Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
This thesis investigates three biologically inspired operations: prefix-suffix duplication, bounded prefix-suffix duplication, and prefix-suffix-square completion. Duplication, a common genetic mutation, involves repeating DNA sequences and…
So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly…
The grammars used in grammar-based Genetic Programming (GP) methods have a significant impact on the quality of the solutions generated since they define the search space by restricting the solutions to its syntax. In this work, we propose…
Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…