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In this article, we provide three coalgebraic characterizations of the class of context-free languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying output-derivative pairs. Final…
Complex machine learning algorithms are used more and more often in critical tasks involving text data, leading to the development of interpretability methods. Among local methods, two families have emerged: those computing importance…
This paper describes an abstract machine for linguistic formalisms that are based on typed feature structures, such as HPSG. The core design of the abstract machine is given in detail, including the compilation process from a high-level…
The functional correspondence is a manual derivation technique transforming higher-order evaluators into the semantically equivalent abstract machines. The transformation consists of two well-known program transformations: translation to…
The fractional polylogarithms, depending on a complex parameter $\a$, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presentation, we show that the fractional…
Large Language Models (LLMs) equipped with external tools have demonstrated enhanced performance on complex reasoning tasks. The widespread adoption of this tool-augmented reasoning is hindered by the scarcity of domain-specific tools. For…
We discuss a new approach to functional interpretations based on uniform quantification and relativization. The uniform quantification in the background permits a more penetrating analysis of principles related to collection and…
Students find their first course in Formal Languages and Automata Theory challenging. In addition to the development of formal arguments, most students struggle to understand nondeterministic computation models. In part, the struggle stems…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
We give a Kleene-type operational characterization of Muller context-free languages (MCFLs) of well-ordered and scattered words.
Morphological tasks use large multi-lingual datasets that organize words into inflection tables, which then serve as training and evaluation data for various tasks. However, a closer inspection of these data reveals profound…
Partiality is a natural phenomenon in computability that we cannot get around. So, the question is whether we can give the areas where partiality occurs, that is, where non-termination happens, more structure. In this paper we consider…
The valence of a function $f$ at a point $w$ is the number of distinct, finite solutions to $f(z) = w$. Let $f$ be a complex-valued harmonic function in an open set $R \subseteq \mathbb{C}$. Let $S$ denote the critical set of $f$ and $C(f)$…
This paper explains how any nondeterministic automaton for a regular language $L$ gives rise to a one-dimensional oriented Topological Quantum Field Theory (TQFT) with inner endpoints and zero-dimensional defects labelled by letters of the…
Multi-task learning (MTL) aims to improve the performance of multiple related prediction tasks by leveraging useful information from them. Due to their flexibility and ability to reduce unknown coefficients substantially, the…
Adapting pretrained large language models (LLMs) to various downstream tasks in tens or hundreds of human languages is computationally expensive. Parameter-efficient fine-tuning (PEFT) significantly reduces the adaptation cost, by tuning…
Lately, there have been intensive studies on strengths and limitations of nonuniform families of promise decision problems solvable by various types of polynomial-size finite automata families, where ``polynomial-size'' refers to the…
We introduce characteristic functions for certain contractive liftings of row contractions. These are multi-analytic operators which classify the liftings up to unitary equivalence and provide a kind of functional model. The most important…
Over recent years, Federated Learning (FL) has proven to be one of the most promising methods of distributed learning which preserves data privacy. As the method evolved and was confronted to various real-world scenarios, new challenges…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html ) is a research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more traditionally been.…