ARE SEARCH AND DECISION PROBLEMS COMPUTATIONALLY EQUIVALENT?

From the point of view of sequential polynomial time computation, the answer to the question in the title is 'yes'. However, from the point of view of fast parallel computation, the answer is not so clear. Many of the sequential algorithms that were 'marked off' as being 'inherently sequential' embed within them the self-reducibility process. Can this inherently sequential process by parallelized? To study this problem, we define an abstract setting (namely that of an independence system) in which one, universal search problem captures all combinatorial search problems. We consider several natural decision and function oracles to which this search problem may be reduced.