PACCAP · Problems in Algebraic Complexity and Complexity of Algebraic Problems
7РП — „Хора“ (Действия „Мария Кюри“)
- Период
- 2009-08-01 → 2012-07-31
- Финансиране от ЕС
- 173 416 €
- Участници
- 1
- Схема
- MC-IOF
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Накратко на български
Алгебричните версии на проблема „P ≠ NP ?“ изследват дали е по-лесно да се провери едно доказателство, отколкото да се открие такова. Работата по тези версии може да помогне за разбирането на един от най-трудните отворени въпроси в математиката и информатиката.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Problems in Algebraic Complexity and Complexity of Algebraic Problems
The “P ≠ NP ?” problem is widely recognized as one of the most important and challenging open problems in contemporary mathematics and computer science. Is it easier to check the proof of a statement than to find such a proof when it exists? The general belief is that this question admits a positive answer, i.e., that P is strictly included in NP. Unfortunately, this intuition is still not supported by a proof in spite of 35 years of intensive research. Given the difficulty of this problem, algebraic versions of “P ≠ NP ?” have been proposed. The hope is that these algebraic versions of the problem should be easier to solve than the original one.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
The P=NP? problem is widely recognized as one of the most important and challenging open problems in contemporary mathematics and computer science. The general belief is that P differs from NP. Unfortunately, this intuition is still not supported by a proof in spite of 35 years of intensive research. Given the difficulty of this problem, algebraic versions of P=NP? have been proposed. The hope is that these algebraic versions of the problem should be easier to solve than the original one. The two main algebraic versions of P=NP? are due to Valiant and to Blum-Shub-Smale. The Blum-Shub-Smale's model deals with computation over the ordered ring of the real numbers whereas the Valiant's model does not deal with decision problems but with polynomial evaluation. In algebraic complexity theory the main focus of this project will be on the study of the relations between Valiant's model, the Blum-Shub-Smale model, and the discrete model of computation. Another focus will be on the complexity of problems from algebraic geometry and from combinatorial optimization, such as linear programming. This research will begin in 2009 in Toronto. A program on Foundational of Computational Mathematics should be held at the Fields Institute in Toronto during the Fall semester. This program should attract many of the best specialists of this research area. Participation in this program is a major contribution to the Training component of the PACCAP project. The project will continue at the computer science department of the University of Toronto, which has a very strong Theory Group. The returning institution is Ecole Normale Supérieure de Lyon, where many of the future French theoretical computer scientist are studying. The skills developped in the PACCAP project will be used there both forresearch and teaching.
Оригинален текст от CORDIS (на английски).
Участници
- ECOLE NORMALE SUPERIEURE DE LYON · LyonКоординаторФранция
Връзки
Данни: CORDIS, © Европейски съюз