Can every set in P be solved in polylogarithmic space? We show that this question is equivalent to asking whether the classes PSPACE and EXPTIME are always equal under relativization. We use an oracle access mechanism that is fair, in the sense that it maintains all known relationships between unrelativized PSPACE and EXPTIME.
CitationGavaldà, R. A positive relativization of polynomial time vs. polylog space. 1991.