Related papers: Numeration Systems: a Link between Number Theory a…
We explore the behaviour emerging from learning agents repeatedly interacting strategically for a wide range of learning dynamics, including $Q$-learning, projected gradient, replicator and log-barrier dynamics. Going beyond the better…
We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata)…
Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we…
Much theoretical work has described the ability of transformers to represent formal languages. However, linking theoretical results to empirical performance is not straightforward due to the complex interplay between the architecture, the…
The paper deals with combinatorial and stochastic structures of cubical token systems. A cubical token system is an instance of a token system, which in turn is an instance of a transition system. It is shown that some basic results of…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
Futrell and Mahowald (2025) frame the success of neural language models (LMs) as supporting gradient, usage-based linguistic theories. I argue that LMs can also instantiate theories based on formal structures - the types of theories seen in…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…
The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…
Ambiguity remains a fundamental challenge in Natural Language Processing (NLP) due to the inherent complexity and flexibility of human language. With the advent of Large Language Models (LLMs), addressing ambiguity has become even more…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
Characterizing the computational power of neural network architectures in terms of formal language theory remains a crucial line of research, as it describes lower and upper bounds on the reasoning capabilities of modern AI. However, when…
Coalgebra is a currently quite active field, which aims to look at generic state-based systems (most prominently automata) from a very abstract point of view, mainly using tools from category theory. One of its achievements is to give a…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
Computational experiments have emerged as a valuable method for studying complex systems, involving the algorithmization of counterfactuals. However, accurately representing real social systems in Agent-based Modeling (ABM) is challenging…
For the first time, we have introduced the concept of N-groups, N-semigroups, N-loops, and N-groupoids. We also define a mixed N-algebraic structure. The main aim of this book is to attract young mathematicians to this interesting field. It…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
While artificial intelligence (AI) technology is becoming increasingly popular, its underlying mechanisms tend to remain opaque to most people. To address this gap, the field of AI literacy aims to develop various resources to teach people…
We introduce regular language states, a family of quantum many-body states. They are built from a special class of formal languages, called regular, which has been thoroughly studied in the field of computer science. They can be understood…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…