When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.09421.8
URN: urn:nbn:de:0030-drops-24112
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Buhrman, Harry ; Fortnow, Lance ; Santhanam, Rahul

Unconditional Lower Bounds against Advice

09421.SanthanamRahul.Paper.2411.pdf (0.2 MB)


We show several unconditional lower bounds for exponential time classes against polynomial time classes with advice, including: (1) For any constant c, NEXP not in P^{NP[n^c]} (2) For any constant c, MAEXP not in MA/n^c (3) BPEXP not in BPP/n^{o(1)}.

It was previously unknown even whether NEXP in NP/n^{0.01}. 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 in i.o.NP, which provides evidence that this is not possible with current techniques.

BibTeX - Entry

  author =	{Buhrman, Harry and Fortnow, Lance and Santhanam, Rahul},
  title =	{{Unconditional Lower Bounds against Advice}},
  booktitle =	{Algebraic Methods in Computational Complexity},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9421},
  editor =	{Manindra Agrawal and Lance Fortnow and Thomas Thierauf and Christopher Umans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-24112},
  doi =		{10.4230/DagSemProc.09421.8},
  annote =	{Keywords: Advice, derandomization, diagonalization, lower bounds, semantic classes}

Keywords: Advice, derandomization, diagonalization, lower bounds, semantic classes
Collection: 09421 - Algebraic Methods in Computational Complexity
Issue Date: 2010
Date of publication: 19.01.2010

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