Logspace Reducibility: Models and Equivalences

Abstract

We study the relative computational power of logspace reduction models. In particular, we study the relationships between one-way and two-way oracle tapes, resetting of the oracle head, and blanking of the oracle tape. We show that oracle models letting information persist between queries can be quite powerful, even if the information is not readable by the querying machine. We show that logspace f(n)-Turing reductions are stronger than polynomial-time f(n)-Turing reductions when f(n) = ω(log n), and that this is optimal if P = L.