Projektbeschreibung
Lösung für hartnäckige Probleme der Zufälligkeitsextraktor-Theorie in Sicht
Hochwertige Zufälligkeit hat zentrale Bedeutung für die Informatik. Zum Beispiel werden in der Kryptografie Zufälligkeitsextraktoren angewendet, um aus halbgeheimen Quellen geheime und zufällige Schlüssel zu erzeugen. Im Allgemeinen handelt es sich bei Zufälligkeitsextraktoren um Algorithmen, die eine schwach zufällige Quelle und einen wirklich zufälligen Anfangswert in eine gleichmäßige Verteilung von Zufallszahlen umwandeln. Das EU-finanzierte Projekt EXT plant die Auslotung einiger der wichtigsten offenen Probleme der Zufälligkeitsextraktor-Theorie. Es wird aufbauend auf erfolgreichen Ergebnissen früherer Forschungsvorhaben auf diesem Gebiet Verfahren der Zufälligkeitsextraktor-Theorie auf drei sorgfältig ausgewählte Probleme anwenden: Derandomisierung raumbegrenzter Berechnungen, Ramsey-Graphen-Konstruktionen und lokal dekodierbare Codes.
Ziel
"Randomness extractors are central in theoretical computer science and have a huge impact in complexity theory, error correcting codes, and cryptography to name a few. Informally, a randomness extractor is an algorithm that ""purifies"" the randomness of an imperfect random source by extracting from it a sequence of uniform and independent random bits. The myriad of applications make randomness extractor theory a vibrant and exciting research field with a major impact. Over the last few years, there has been a flurry of progress on deep long-standing open problems in the field and the PI's work played a key role in this development. Several novel ideas were introduced which give hope that other long-standing open problems in the field can be resolved. Moreover, the new techniques raise new and intriguing questions. In this research, we propose to study some of the most important open problems in randomness extractor theory: classic as well as the new challenges that arise. Moreover, we propose to apply results and techniques from randomness extract theory to three carefully chosen problems with a huge impact on their respective fields: (1) derandomization of space-bounded computation; (2) Ramsey graph constructions; and (3) locally decodable codes. Progress on any of these problems would be ground breaking. Despite the significant challenge, we believe that we are in a unique place to pursue these long-standing open problems both within randomness extractors theory and beyond. Indeed, as mentioned, the PI's work on randomness extractors was pivotal to the exciting progress in the field. Moreover, the PI obtained a breakthrough result on Ramsey graphs construction and the first improvement in 25 years on a problem related to derandomization of space-bounded computation. Both results were obtained using machinery from randomness extractor theory."
Wissenschaftliches Gebiet
Programm/Programme
Thema/Themen
Finanzierungsplan
ERC-STG - Starting GrantGastgebende Einrichtung
69978 Tel Aviv
Israel