Related papers: Automata and rational expressions
In my book "Algorithmic Information Theory" I explain how I constructed a million-character equation that proves that there is randomness in arithmetic. My book only includes a few pages from the monster equation, and omits the software…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
This volume contains revised versions of the papers selected for the first volume of the Online Handbook of Argumentation for AI (OHAAI). Previously, formal theories of argument and argument interaction have been proposed and studied, and…
The volume comprises the proceedings of the Third Workshop on Agents and Robots for reliable Engineered Autonomy (AREA 2023), held alongside the 26th European Conference on Artificial Intelligence (ECAI 2023). It explores the convergence of…
We extend the functorial approach to automata by Colcombet and Petri\c{s}an [arXiv:1712.07121] from the category of sets to any elementary topos with a natural number object and establish general Myhill-Nerode theorems in our setting. As a…
We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion,…
We establish an assume-guarantee (AG) framework for compositional reasoning about multi-objective queries in parametric probabilistic automata (pPA) - an extension to probabilistic automata (PA), where transition probabilities are functions…
This article is a brief survey of the theory of topological modular forms (TMF) and the theory of topological automorphic forms (TAF). It will be a chapter in forthcoming "Handbook of Homotopy Theory" edited by Haynes Miller.
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinement and compositional reasoning. In recent years, quantitative variants of modal…
Data automata on data words is a decidable model proposed by Boja\'nczyk et al. in 2006. Class automata, introduced recently by Boja\'nczyk and Lasota, is an extension of data automata which unifies different automata models on data words.…
Large Language Model (LLM) based agents have demonstrated proficiency in multi-step interactions with graphical user interfaces (GUIs). While most research focuses on improving single-task performance, practical scenarios often involve…
This paper grew out of three tutorial lectures on automatic structures given by the first author at the Logic Colloquium 2007. We discuss variants of automatic structures related to several models of computation: word automata, tree…
The problem of characterizing which automatic sets of integers are stable is here solved. Given a positive integer $d$ and a subset $A\subseteq \mathbb{Z}$ whose set of representations base $d$ is recognized by a finite automaton, a…
In mathematics, LaTeX is the de facto standard to prepare documents, e.g., scientific publications. While some formulae are still developed using pen and paper, more complicated mathematical expressions used more and more often with…
This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…
Given a member A of the class of non-deterministic timed automata with silent transitions (eNTA), we effectively compute its timestamp: the set of all pairs (time value, action) of all observable timed traces of A, a generalization of the…
We propose an automaton model which is a combination of symbolic and register automata, i.e., we enrich symbolic automata with memory. We call such automata Register Match Automata (RMA). RMA extend the expressive power of symbolic…
We define compact automata and show that every language has a unique minimal compact automaton. We also define recognition of languages by compact left semitopological monoids and construct the analogue of the syntactic monoid in this…
As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…