reducibility, randomness, and intractibility (abstract)
The method of showing a problem NP-complete by polynomial reduction is one of the most elegant and productive in our theory ([ 1 ], [ 3 ]). It is a means of providing compelling evidence that a problem in NP is not in P. In this paper we will demonstrate new methods for showing this. Our methods, based on a new notion of reducibility (gamma-reducibility) are apparently of more general applicability than that of polynomial reduction and are intended to be of practical value to researchers in the field. We use our methods to demonstrate (i.e., give compelling evidence) that some natural problems in NP which are not known to be NP-complete are, nonetheless, not in P.
randomization abstraction method polynomial reduction theory evidence paper demonstrate general applications practical value research use completeness