We show several unconditional lower bounds for exponential time classes against polynomial time classes with advice, including: 1. For any constant c, NEXP 6 PNP[nc]/nc 2. For any constant c, MAEXP 6 MA/nc 3. BPEXP 6 BPP/no(1) It was previously unknown even whether NEXP NP/n0.01. For the probabilistic classes, no lower bounds for uniform exponential time against advice were known before. We also consider the question of whether these lower bounds can be made to work on almost all input lengths rather than on infinitely many. We give an oracle relative to which NEXP i.o.NP, which provides evidence that this is not possible with current techniques.

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Dagstuhl Seminar Proceedings
Algebraic Methods in Computational Complexity, 2009
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Buhrman, H., Fortnow, L., & Santhanam, R. (Rahul). (2010). Unconditional Lower Bounds Against Advice. In Dagstuhl Seminar Proceedings. doi:10.4230/DagSemProc.09421.8