If the result stands, it would prove that the two classes P and NP are not identical, and impose severe limits on what computers can accomplish – implying that many tasks may be fundamentally, irreducibly complex.
For some problems – including factorisation – the result does not clearly say whether they can be solved quickly. But a huge sub-class of problems called "NP-complete" would be doomed. A famous example is the travelling salesman problem – finding the shortest route between a set of cities. Such problems can be checked quickly, but if P ≠ NP then there is no computer program that can complete them quickly from scratch.
Complexity theorists have given a favourable reception to Deolalikar's draft paper, but when the final version is released in a week's time the process of checking it will intensify.
Friday, August 20, 2010
P ≠ NP? Limits on Computing?
An August 10th article in the NewScientist titled, P ≠ NP? It's bad news for the power of computing, reports that a mathematician Vinay Deolalikar has perhaps solved a major computational problem.