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Paper:

TR04-014 | 26th November 2003 00:00

Languages to diagonalize against advice classes

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TR04-014
Authors: Chris Pollett
Publication: 16th February 2004 13:41
Downloads: 1119
Keywords: 


Abstract:

Variants of Kannan's Theorem are given where the circuits of
the original theorem are replaced by arbitrary recursively presentable
classes of languages that use advice strings and satisfy certain mild
conditions. These variants imply that $\DTIME(n^{k'})^{\NE}/n^k$
does not contain $\PTIME^{\NE}$, $\DTIME(2^{n^{k'}})/n^k$ does
not contain $\EXP$, $\SPACE(n^{k'})/n^k$ does not contain $\PSPACE$,
uniform $\TC^0/n^k$ does not contain $\CH$, and uniform $\ACC/n^k$
does not contain $\ModPH$. Consequences for selective sets are also
obtained. In particular, it is shown that
$\R^{DTIME(n^k)}_T(\NP$-$\sel)$ does not contain $\PTIME^{\NE}$,
$\R^{DTIME(n^k)}_T(\PTIME$-$\sel)$ does not contain $\EXP$, and
that $\R^{DTIME(n^k)}_T(\L$-$\sel)$ does not contain $\PSPACE$.
Finally, a circuit size hierarchy theorem is established.



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