Related papers: Learning Regular Languages over Large Ordered Alph…

It is known that an ordinal is the order type of the lexicographic ordering of a regular language if and only if it is less than omega^omega. We design a polynomial time algorithm that constructs, for each well-ordered regular language L…

Algorithm selection, a critical process of automated machine learning, aims to identify the most suitable algorithm for solving a specific problem prior to execution. Mainstream algorithm selection techniques heavily rely on problem…

These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…

Automata over infinite alphabets have emerged as a convenient computational model for processing structures involving data, such as nonces in cryptographic protocols or data values in XML documents. We introduce active learning methods for…

Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a…

A generalization of numeration system in which the set N of the natural numbers is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. Here we show that if P belonging to Q[x]…

Language is essentially a complex, intricate system of human expressions governed by grammatical rules. It poses a significant challenge to develop capable AI algorithms for comprehending and grasping a language. As a major approach,…

A major target of linguistics and cognitive science has been to understand what class of learning systems can acquire the key structures of natural language. Until recently, the computational requirements of language have been used to argue…

Language learning refers to the problem of inferring a mathematical model which accurately represents a formal language. Many language learning algorithms learn by asking certain types of queries about the language being modeled. Language…

This work is a survey of the main results reported for the degree of extension of two models defining non-regular languages, namely the context-free grammar and the extended automaton over groups. More precisely, we recall the main results…

In this paper, we study the ability of large language models to learn specific mathematical rules such as distributivity or simplifying equations. We present an empirical analysis of their ability to generalize these rules, as well as to…

Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a finite alphabet A. For these systems, we obtain a…

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…

Optimization algorithms and large language models (LLMs) enhance decision-making in dynamic environments by integrating artificial intelligence with traditional techniques. LLMs, with extensive domain knowledge, facilitate intelligent…

Although current large language models are complex, the most basic specifications of the underlying language generation problem itself are simple to state: given a finite set of training samples from an unknown language, produce valid new…

We propose a novel approach for decision making problems leveraging the generalization capabilities of large language models (LLMs). Traditional methods such as expert systems, planning algorithms, and reinforcement learning often exhibit…

Conventional rule learning algorithms aim at finding a set of simple rules, where each rule covers as many examples as possible. In this paper, we argue that the rules found in this way may not be the optimal explanations for each of the…

Prior work has shown that large language models (LLMs) often converge to accurate input embedding for numbers, based on sinusoidal representations. In this work, we quantify that these representations are in fact strikingly systematic, to…

Cognitive systems generally require a human to translate a problem definition into some specification that the cognitive system can use to attempt to solve the problem or perform the task. In this paper, we illustrate that large language…

Large language models (LLM) are advanced AI systems trained on extensive textual data, leveraging deep learning techniques to understand and generate human-like language. Today's LLMs with billions of parameters are so huge that hardly any…