Description du projet
Faire avancer la théorie de la complexité informatique
La théorie de la complexité examine les limites inférieure et supérieure de la complexité des modèles informatiques concrets. Cependant, les chercheurs ont accompli très peu de progrès pour prouver la forte complexité des limites inférieures et ont découvert plusieurs résultats notables à propos des barrières. Bien qu’ils constituent un obstacle important, ces résultats ont également fait ressortir de nouvelles propriétés structurelles de la complexité des limites inférieures reliant les limites inférieures à la construction d’algorithmes d’apprentissage efficaces, de la cryptographie ou des résultats d’indépendance dans la logique mathématique. Le projet MCT, financé par l’UE, vise à poursuivre le développement de ces liaisons structurelles et des propriétés théoriques liées à la complexité des problèmes de complexité. Pour ce faire, il se concentrera sur l’«amplification de la dureté» (hardness magnification en anglais) et la théorie structurelle. Ces travaux permettront de mieux comprendre les questions centrales de la théorie de la complexité informatique.
Objectif
The goal of the project is to advance our understanding of the central questions in Computational Complexity Theory such as the famous P versus NP problem.
Complexity Theory approaches questions about efficiency of computation by investigating lower and upper bounds on the complexity of concrete computational models such as Boolean circuits or propositional proof systems. Unfortunately, even after several decades of intense research the progress on the question of proving strong complexity lower bounds remains very incremental. In fact, several significant barrier results have been discovered, partially explaining the complexity of establishing complexity lower bounds.
While the barrier results presented a serious obstacle they also revealed new structural properties of complexity lower bounds connecting lower bounds to the construction of efficient learning algorithms, cryptography or independence results in mathematical logic. The present project continues the development of these structural connections and complexity-theoretic properties of problems about complexity, which we shortly refer to as Metacomputational Complexity Theory.
The objectives of the project can be divided into two groups.
1. Hardness magnification, exploring limits and consequences of an emerging theory of hardness magnification which arouse recently from investigations of metacomputational aspects of circuit lower bounds and received a lot of attention as a promising approach overcoming previously existing barriers for proving complexity lower bounds.
2. Structural theory, strengthening and generalizing connections between the methods for proving lower bounds and other central concepts of computer science, such as efficient learning algorithms, cryptographic primitives and automatizability of propositional proof systems, through the lens of mathematical logic.
Champ scientifique
Programme(s)
Régime de financement
MSCA-IF-EF-ST - Standard EFCoordinateur
OX1 2JD Oxford
Royaume-Uni