Generalised Tree Automata, Monadic Second Order Logic and Transfer Principles in Combinatorial Limits

Información del proyecto

FINTOINF

Identificador del acuerdo de subvención: 101023298

DOI

10.3030/101023298

Proyecto cerrado

Fecha de la firma de la CE 16 Marzo 2021

Fecha de inicio 1 Abril 2021

Fecha de finalización 31 Marzo 2023

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 196 707,84

Aportación de la UE

€ 196 707,84

Coordinado por

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France

Descripción del proyecto

Métodos nuevos para preguntas sin resolver fundamentales en matemáticas e informática

La lógica de predicados monádicos de segundo orden es un tipo de lógica matemática de gran importancia para expresar las especificaciones formales de las propiedades de los grafos, así como para la teoría de autómatas, que describe máquinas autopropulsadas, tanto abstractas como reales. Durante el último medio siglo, los científicos han logrado numerosos avances en la teoría de predicados monádicos de segundo orden, pero aún quedan preguntas sin resolver fundamentales. El objetivo del proyecto FINTOINF, que cuenta con el apoyo de las Acciones Marie Skłodowska-Curie, es abordar dos de estas preguntas que, a pesar de los múltiples trabajos e investigaciones, aún siguen sin resolver, a saber: la conjetura de Shelah, sobre la teoría del orden de predicados monádicos, y los límites combinatorios contables.

Objetivo

The project will concentrate on two main directions (MD), which are connected through them both relying on Monadic Second Order (MSO) and its variants. (MD 1) Shelah's conjecture. In his celebrated 1975 paper Shelah proved that the monadic second order theory (MSO) of the real order is undecidable. He conjectured in his Conjecture 7B that Conjecture: MSO of the real order where the second order quantifier ranges only over Borel sets, is decidable. In spite of important efforts on this question in both mathematics and computer science community, the conjecture is still open. Many strategies, including the one suggested by Shelah in his paper (to use Borel determinacy) have been tried. We propose to study this question using the recent methods of the generalised descriptive set theory and the generalised automata that we intend to develop. This is novel and might lead to important advances and the solution. (MD2) Countable combinatorial limits. Since the work of Lovasz and others in his group around 2006, a new area of discrete mathematics emerged: the combinatorial limits. This fast growing area aroused much interest and found many applications Its first development was that of a graphon, which is an uncountable limit of a sequence of finite graphs, but there have been several others. It is always important to understand the transfer properties of statements between the sequence forming the limit and the limit itself. The question has been considered through ultrapowers and through topology and Stone's pairings. None suffices for the transfer of MSO sentence. We propose to study that transfer through the novel notion of a countable model where the notion of satisfaction has been changed so that the countable model reflects the structure of the sequence of finite models that were used to obtain the uncountable combinatorial limit. In this sense we obtain a countable combinatorial limit which we study using the methods of finite model theory.

Ámbito científico (EuroSciVoc)

• ciencias naturales › matemáticas › matemáticas puras › matemáticas discretas › lógica matemática

Palabras clave

• Uncountable tree orders and algorithms
• Monadic Second Order logic
• Combinatorial Limits
• Transfer Principles

Programa(s)

• H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions PROGRAMA PRINCIPAL
  
• H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
  

Tema(s)

• MSCA-IF-2020 - Individual Fellowships
  

Régimen de financiación

MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)

Convocatoria de propuestas

H2020-MSCA-IF-2020

Coordinador

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS

• Aportación neta de la UEn: € 196 707,84
• Dirección: RUE MICHEL ANGE 3 ; 75794 PARIS ; Francia
• Tipo de actividad: Research Organisations
• Coste total: € 196 707,84