ECCC-Report TR10-135https://eccc.weizmann.ac.il/report/2010/135Comments and Revisions published for TR10-135en-usThu, 23 Dec 2010 12:38:53 +0200
Revision 2
| In a World of P=BPP |
Oded Goldreich
https://eccc.weizmann.ac.il/report/2010/135#revision2We show that proving results such as BPP=P essentially
necessitate the construction of suitable pseudorandom generators
(i.e., generators that suffice for such derandomization results).
In particular, the main incarnation of this equivalence
refers to the standard notion of uniform derandomization
and to the corresponding pseudorandom generators
(i.e., the standard uniform notion of ``canonical derandomizers'').
This equivalence bypasses the question of which hardness assumptions
are required for establishing such derandomization results,
which has received considerable attention in the last decade or so
(starting with Impagliazzo and Wigderson [JCSS, 2001]).
We also identify a natural class of search problems
that can be solved by deterministic polynomial-time
reductions to BPP. This result is instrumental to the
construction of the aforementioned pseudorandom generators
(based on the assumption BPP=P), which is actually a
reduction of the ``construction problem'' to BPP.
Caveat: Throughout the text, we abuse standard notation
by letting BPP, P etc denote classes of promise problems.
Thu, 23 Dec 2010 12:38:53 +0200https://eccc.weizmann.ac.il/report/2010/135#revision2
Revision 1
| In a World of P=BPP |
Oded Goldreich
https://eccc.weizmann.ac.il/report/2010/135#revision1We show that proving results such as BPP=P essentially
necessitate the construction of suitable pseudorandom generators
(i.e., generators that suffice for such derandomization results).
In particular, the main incarnation of this equivalence
refers to the standard notion of uniform derandomization
and to the corresponding pseudorandom generators
(i.e., the standard uniform notion of ``canonical derandomizers'').
This equivalence bypasses the question of which hardness assumptions
are required for establishing such derandomization results,
which has received considerable attention in the last decade or so
(starting with Impagliazzo and Wigderson [JCSS, 2001]).
We also identify a natural class of search problems
that can be solved by deterministic polynomial-time
reductions to BPP. This result is instrumental to the
construction of the aforementioned pseudorandom generators
(based on the assumption BPP=P), which is actually a
reduction of the ``construction problem'' to BPP.
Caveat: Throughout the text, we abuse standard notation
by letting BPP, P etc denote classes of promise problems.
Sat, 28 Aug 2010 10:57:00 +0300https://eccc.weizmann.ac.il/report/2010/135#revision1
Paper TR10-135
| In a World of P=BPP |
Oded Goldreich
https://eccc.weizmann.ac.il/report/2010/135We show that proving results such as BPP=P essentially
necessitate the construction of suitable pseudorandom generators
(i.e., generators that suffice for such derandomization results).
In particular, the main incarnation of this equivalence
refers to the standard notion of uniform derandomization
and to the corresponding pseudorandom generators
(i.e., the standard uniform notion of ``canonical derandomizers'').
This equivalence bypasses the question of which hardness assumptions
are required for establishing such derandomization results,
which has received considerable attention in the last decade or so
(starting with Impagliazzo and Wigderson [JCSS, 2001]).
We also identify a natural class of search problems
that can be solved by deterministic polynomial-time
reductions to BPP. This result is instrumental to the
construction of the aforementioned pseudorandom generators
(based on the assumption BPP=P), which is actually a
reduction of the ``construction problem'' to BPP.
Caveat: Throughout the text, we abuse standard notation
by letting BPP, P etc denote classes of promise problems.
Tue, 24 Aug 2010 15:48:20 +0300https://eccc.weizmann.ac.il/report/2010/135