Sunday, August 15, 2010

My criteria for what I consider a serious proof for the P vs NP problem

In light of Deolalikar's proof for P!=NP , Any valid resolution of the P vs NP problem must shed light and offer new insights into some of the fundamental concepts in mathematics and computer science. We want to really understand the true relationship between concepts like efficient computation of functions, randomness, and the computational nature of proofs. Why are some functions hard to compute while others are easy? What does constitute a random function? The ultimate resolution of the P vs NP problem must provide new insights into the nature of randomness and how it relates to efficient computation.

In my opinion, what is needed is a paradigm shift. This is what the history of scientific revolutions taught us. I believe we need to abandon the tradition of using polynomial functions to define the various notions of efficient computation. Invoking polynomial growth rates could be a symptom of paradigm blindness. I call it the Polynomial Disease.

No comments:

Post a Comment