Wednesday, February 4

Problem Reductions Continued

We discussed problem reductions with some examples.  The notion of a "worthy problem" (Papadimitriou's term) was one of the topics.  This led to a definition of "complete problem" as capturing the idea of a "worthy problem" (one that represents a "hardest" member of the class.

We then explored what it meant for a class to be closed under reduction, which is important for demonstrating a complete problem in a class.  This led finally to the observation that L, NL, P, NP, coNP, PSPACE, and EXP are all closed under reductions and can have compllete problems.