Related papers: Generic Results for Concatenation Hierarchies
We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal interpretations and some research directions.…
The mathematical modeling of generics in Java and other similar nominally-typed object-oriented programming languages is a challenge. In this short paper we present the outline of a novel order-theoretic approach to modeling generics, in…
When we investigate a type system, it is helpful if we can establish the well-foundedness of types or terms with respect to a certain hierarchy, and the Extended Calculus of Constructions (called $ECC$, defined and studied comprehensively…
Sequence-to-sequence transduction is the core problem in language processing applications as diverse as semantic parsing, machine translation, and instruction following. The neural network models that provide the dominant solution to these…
This is a short survey of the progress on the congruence subgroup problem since the sixties when the first major results on the integral unimodular groups appeared. It is aimed at the non-specialists and avoids technical details.
This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
In the constrained synchronization problem we ask if a given automaton admits a synchronizing word coming from a fixed regular constraint language. We show that intersecting a given constraint language with an ideal language decreases the…
According to the principle of compositional generalization, the meaning of a complex expression can be understood as a function of the meaning of its parts and of how they are combined. This principle is crucial for human language…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal…
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
The field of Natural Language Processing has experienced a dramatic leap in capabilities with the recent introduction of huge Language Models. Despite this success, natural language problems that involve several compounded steps are still…
Question answering models struggle to generalize to novel compositions of training patterns, such to longer sequences or more complex test structures. Current end-to-end models learn a flat input embedding which can lose input syntax…
In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we…
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. In the past, two independent hierarchies have been obtained for external and internal…
Deep neural networks drive the success of natural language processing. A fundamental property of language is its compositional structure, allowing humans to systematically produce forms for new meanings. For humans, languages with more…
Aggregating different pieces of similar information is necessary to generate concise and easy to understand reports in technical domains. This paper presents a general algorithm that combines similar messages in order to generate one or…
Systems now exist which are able to compile unification grammars into language models that can be included in a speech recognizer, but it is so far unclear whether non-trivial linguistically principled grammars can be used for this purpose.…
The downward and upward closures of a regular language $L$ are obtained by collecting all the subwords and superwords of its elements, respectively. The downward and upward interiors of $L$ are obtained dually by collecting words having all…