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ECCC
2011

Two Comments on Targeted Canonical Derandomizers

13 years 5 months ago
Two Comments on Targeted Canonical Derandomizers
We revisit the notion of a targeted canonical derandomizer, introduced in our recent ECCC Report (TR10-135) as a uniform notion of a pseudorandom generator that suffices for yielding BPP = P. The original notion was derived (as a variant of the standard notion of a canonical derandomizer) by providing both the distinguisher and the generator with the same auxiliaryinput. Here we take one step further and consider pseudorandom generators that fool a single circuit that is given to them as auxiliary input. Building on TR10-135, we show that such pseudorandom generators exist if and only if BPP = P, which means that they exist if and only if targeted canonical derandomizers (of exponential stretch, as in TR10-135) exist. We also relate such targeted canonical derandomizer to targeted hitters, which are the analogous canonical derandomizers for RP.
Oded Goldreich
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where ECCC
Authors Oded Goldreich
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