The class NP captures the difficulty of finding certificates. However, in many contexts, one is interested not just in a single certificate, but actually counting the number of certificates. In this manuscript we look at a famous result involving #P, (pronounced “sharp p”), a complexity class that captures this notion. Counting problems arise in diverse fields, often in situations having to do ...

Being NP complete has been widely interpreted as being computationally intractable But NP completeness is a worst case concept Some NP complete problems are easy on average but some may not be How is one to know whether an NP complete problem is di cult on average The theory of average case computational complexity initiated by Levin about ten years ago is devoted to studying this problem This ...