On reductions to sets that avoid EXPSPACE

Abstract

A s e t B is called EXPSPACE-avoiding, i f e v ery subset of B in EXPSPACE is sparse. Sparse sets and sets of high information density (called HIGH sets in 5]) are shown to be EXPSPACE-avoiding. Investigating the complexity o f sets A in EXPSPACE that honestly reduce to EXPSPACE-avoiding sets, we show that if the reducibility used has a property, c a l l e d range-constructibility, then A must also reduce to a sparse set under the same reducibility.