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This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
We show that for any monoid M, the family of languages accepted by M-automata (or equivalently, generated by regular valence grammars over M) is completely determined by that part of M which lies outside the maximal ideal. Hence, every such…
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
Cross-lingual word embeddings encode the meaning of words from different languages into a shared low-dimensional space. An important requirement for many downstream tasks is that word similarity should be independent of language - i.e.,…
We investigate a famous decision problem in automata theory: separation. Given a class of language C, the separation problem for C takes as input two regular languages and asks whether there exists a third one which belongs to C, includes…
In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple programming language - representing non-deterministic imperative programs with bounded loops, and arithmetics limited to addition and multiplication - it is possible to…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
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 paper studies the limits of recursive classifications in proof theory and program extraction, using the refined $A$-translation as a central example. The refined $A$-translation, due to Berger, Buchholz, and Schwichtenberg, is based on…
Large language models (LLMs) have shown surprisingly good performance in multilingual neural machine translation (MNMT) even when trained without parallel data. Yet, despite the fact that the amount of training data is gigantic, they still…
Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…
The aim of the paper is to build a connection between two approaches towards categorical language theory: the coalgebraic and algebraic language theory for monads. For a pair of monads modelling the branching and the linear type we defined…
The recent advancements in Transformer-based Language Models have demonstrated significant potential in enhancing the multilingual capabilities of these models. The remarkable progress made in this domain not only applies to natural…
We investigate the complexity of uniform OR circuits and AND circuits of polynomial-size and depth. As their name suggests, OR circuits have OR gates as their computation gates, as well as the usual input, output and constant (0/1) gates.…
The progress made in code modeling has been tremendous in recent years thanks to the design of natural language processing learning approaches based on state-of-the-art model architectures. Nevertheless, we believe that the current…
Learning neural program embeddings is key to utilizing deep neural networks in program languages research --- precise and efficient program representations enable the application of deep models to a wide range of program analysis tasks.…
Recent work shows Large Language Models (LLMs) struggle to understand natural language constraints for various text generation tasks in zero- and few-shot settings. While, in the code domain, there is wide usage of constraints in code…
Recently, code language models have achieved notable advancements in addressing a diverse array of essential code comprehension and generation tasks. Yet, the field lacks a comprehensive deep dive and understanding of the code embeddings of…