Abstract
We show several unconditional lower bounds for exponential time classes against polynomial time classes with advice, including:
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For any constant c, \({\sf NEXP} \not \subseteq {\rm{\sf P}}^{\sf NP[n^c]}/n^c\)
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For any constant c, \({\sf MAEXP} \not \subseteq {\rm {\sf MA}}/n^c\)
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\({\sf BPEXP} \not \subseteq {\sf BPP}/n^{o(1)}\)
It was previously unknown even whether NEXP ⊆ 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 ⊆ io NP, which provides evidence that this is not possible with current techniques.
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Buhrman, H., Fortnow, L., Santhanam, R. (2009). Unconditional Lower Bounds against Advice. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds) Automata, Languages and Programming. ICALP 2009. Lecture Notes in Computer Science, vol 5555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02927-1_18
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