Innovating Works

ANT

Financiado
Automata in Number Theory
Finite automata are fundamental objects in Computer Science, of great importance on one hand for theoretical aspects (formal language theory, decidability, complexity) and on the other for practical applications (parsing). In num... Finite automata are fundamental objects in Computer Science, of great importance on one hand for theoretical aspects (formal language theory, decidability, complexity) and on the other for practical applications (parsing). In number theory, finite automata are mainly used as simple devices for generating sequences of symbols over a finite set (e.g., digital representations of real numbers), and for recognizing some sets of integers or more generally of finitely generated abelian groups or monoids. One of the main features of these automatic structures comes from the fact that they are highly ordered without necessarily being trivial (i.e., periodic). With their rich fractal nature, they lie somewhere between order and chaos, even if, in most respects, their rigidity prevails. Over the last few years, several ground-breaking results have lead to a great renewed interest in the study of automatic structures in arithmetics. A primary objective of the ANT project is to exploit this opportunity by developing new directions and interactions between automata and number theory. In this proposal, we outline three lines of research concerning fundamental number theoretical problems that have baffled mathematicians for decades. They include the study of integer base expansions of classical constants, of arithmetical linear differential equations and their link with enumerative combinatorics, and of arithmetics in positive characteristic. At first glance, these topics may seem unrelated, but, surprisingly enough, the theory of finite automata will serve as a natural guideline. We stress that this new point of view on classical questions is a key part of our methodology: we aim at creating a powerful synergy between the different approaches we propose to develop, placing automata theory and related methods at the heart of the subject. This project provides a unique opportunity to create the first international team focusing on these different problems as a whole. ver más
31/03/2022
CNRS
1M€
Duración del proyecto: 78 meses Fecha Inicio: 2015-09-10
Fecha Fin: 2022-03-31

Línea de financiación: concedida

El organismo H2020 notifico la concesión del proyecto el día 2022-03-31
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-CoG-2014: ERC Consolidator Grant
Cerrada hace 10 años
Presupuesto El presupuesto total del proyecto asciende a 1M€
Líder del proyecto
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE... No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5