Final Report Summary - PACCAP (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.