Related papers: Non-algorithmic theory of randomness
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
We consider the problem of computing the probability of regular languages of infinite trees with respect to the natural coin-flipping measure. We propose an algorithm which computes the probability of languages recognizable by \emph{game…
In this thesis, we study the place of regular languages within the communication complexity setting. In particular, we are interested in the non-deterministic communication complexity of regular languages. We show that a regular language…
We consider a type of long-range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word…
Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…
The standard way to evaluate language models on subjective tasks is through pairwise comparisons: an annotator chooses the "better" of two responses to a prompt. Leaderboards aggregate these comparisons into a single Bradley-Terry (BT)…
Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…
We are motivated by the following question: which data languages admit an active learning algorithm? This question was left open in previous work by the authors, and is particularly challenging for languages recognised by nondeterministic…
Recurrent neural networks are convenient and efficient models for language modeling. However, when applied on the level of characters instead of words, they suffer from several problems. In order to successfully model long-term…
We develop a correspondence between the theory of sequential algorithms and classical reasoning, via Kreisel's no-counterexample interpretation. Our framework views realizers of the no-counterexample interpretation as dynamic processes…
In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics…
We study languages and formal power series associated to (variants of) Hammersley's process. We show that the ordinary Hammersley process yields a regular language and the Hammersley tree process yields deterministic context-free (but…
Today artificial neural networks are applied in various fields - engineering, data analysis, robotics. While they represent a successful tool for a variety of relevant applications, mathematically speaking they are still far from being…
Simple representations of documents based on the occurrences of terms are ubiquitous in areas like Information Retrieval, and also frequent in Natural Language Processing. In this work we propose a logical-probabilistic approach to the…
The rapid advancement of large language model (LLM) technology has led to diverse applications, many of which inherently require randomness, such as stochastic decision-making, gaming, scheduling, AI agents, and cryptography-related tasks.…
This paper focuses on the noiseless complete dictionary learning problem, where the goal is to represent a set of given signals as linear combinations of a small number of atoms from a learned dictionary. There are two main challenges faced…
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
The paper describes a parser of sequences of (English) part-of-speech labels which utilises a probabilistic grammar trained using the inside-outside algorithm. The initial (meta)grammar is defined by a linguist and further rules compatible…
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…
Chinese input recommendation plays an important role in alleviating human cost in typing Chinese words, especially in the scenario of mobile applications. The fundamental problem is to predict the conditional probability of the next word…