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ANT: Automata in Number Theory.

Total cost: EUR 1 438 745

EU contribution: EUR 1 438 745

Objective: 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.

Project completion date : 2020-09-30 12:00:00

Major organization : CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE

Address : 3, rue Michel-Ange

75794 Paris cedex 16

Country :France

Url : http://www.cnrs.fr/

Financier : European Union (EU),

Financier address : European Union (EU)

Rue de la Loi 200/Wetstraat 200,

B-1049 Bruxelles/Brussels,

Belgium

Tel: 32-2-2999696, 2993085

Fax: 32-2-2961749

Url: ec.europa.eu/

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Publication:Mena Report
Date:Nov 25, 2015
Words:385
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