The power of witness reduction

Abstract

Recent results by M. Ogiwara and L.A. Hemachandra (1990) established a connection between functions being hard for a class of functions and functions interacting with the class to effect witness reduction. The author believes that the ability to achieve some form of witness reduction is what makes a function hard for a class of functions. To support this thesis he defines new function classes and obtains results analogous to those of Ogiwara and Hemachandra. He also introduces the notion of randomly hard functions and obtains similar results.<>