Information content and computational complexity of recursive sets

Abstract

An honest function is, roughly speaking, a unary, recursive, and strictly increasing function with a very simple graph. Thus if / is an honest function, then the growth of / reflects the computational complexity of /. The honest elementary degrees are the degree structure induced on the honest functions by the reducibility relation "being (Kalmar) elementary in". (Other subrecursive reducibility relations will also work, for example "being primitive recursive in", but not "being polynomial time computable in the length of input\ "Being polynomial time computable in the input * This paper is in its final form, and no similar paper has been or is being submitted elsewhere.