Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study computational procedures that use both randomness and nondeterminism. Examples are Arthur-Merlin games and approximate counting and sampling of NP-witnesses. The goal of this paper is to derandomize such procedures under the akest possible assumptions. Our main technical contribution allows one to "boost" a given hardness assumption. One special case is a proof that EXP /spl nsube/ NP/poly /spl rArr/ EXP /spl nsube/ P/sub /spl par///sup NP//poly. In words, if there is a problem in EXP that cannot be computed by poly-size nondeterministic circuits then there is one which cannot be computed by poly-size circuits that make non-adaptive NP oracle queries. This in particular shows that the various assumptions used over the last few years by several authors to derandomize Arthur-Merlin games (i.e., show AM = NP) are in fact all equivalent. In addition to simplifying the framework of AM derandomization,  show that this "unified assumption" suffices to de-randomize several other probabilistic procedures. For these results  define two new primitives that  regard as the natural pseudorandom objects associated with approximate counting and sampling of NP-witnesses.  use the "boosting" theorem and hashing techniques to construct these primitives using an assumption that is no stronger than that used to derandomize AM. As a consequence, under this assumption, there are deterministic polynomial time algorithms that use non-adaptive NP-queries and perform the following tasks: 1) approximate counting of NP-witnesses: given a Boolean circuit A, output r such that (1 - /spl epsi/)|A/sup -1/(1)| /spl les/ r les; |A/sup -1/(1)|. 2) pseudorandom sampling of NP-witnesses: given a Boolean circuit A, produce a polynomial-size sample space that is computationally indistinguishable from the uniform distribution over A/sup -1/(1).  also present applications. For example,  observe that Cai's proof that S/sub 2//sup p/ /spl sube/ ZPP/sup NP/ and the learning algorithm of Bshouty et al. can be seen as reductions to sampling that are not probabilistic. As a consequence they can be derandomized under the assumption stated above, which is aker than the assumption that was previously known to suffice.
['Ronen Shaltiel', 'Christopher Umans']
I am writing a research paper on a idea Pseudorandomness for approximate counting and sampling
[{"from": "human", "value": "I am writing a research paper on a idea Pseudorandomness for approximate counting and sampling"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study computational procedures that use both randomness and nondeterminism. Examples are Arthur-Merlin games and approximate counting and sampling of NP-witnesses. The goal of this paper is to derandomize such procedures under the akest possible assumptions. Our main technical contribution allows one to \"boost\" a given hardness assumption. One special case is a proof that EXP /spl nsube/ NP/poly /spl rArr/ EXP /spl nsube/ P/sub /spl par///sup NP//poly. In words, if there is a problem in EXP that cannot be computed by poly-size nondeterministic circuits then there is one which cannot be computed by poly-size circuits that make non-adaptive NP oracle queries. This in particular shows that the various assumptions used over the last few years by several authors to derandomize Arthur-Merlin games (i.e., show AM = NP) are in fact all equivalent. In addition to simplifying the framework of AM derandomization,  show that this \"unified assumption\" suffices to de-randomize several other probabilistic procedures. For these results  define two new primitives that  regard as the natural pseudorandom objects associated with approximate counting and sampling of NP-witnesses.  use the \"boosting\" theorem and hashing techniques to construct these primitives using an assumption that is no stronger than that used to derandomize AM. As a consequence, under this assumption, there are deterministic polynomial time algorithms that use non-adaptive NP-queries and perform the following tasks: 1) approximate counting of NP-witnesses: given a Boolean circuit A, output r such that (1 - /spl epsi/)|A/sup -1/(1)| /spl les/ r les; |A/sup -1/(1)|. 2) pseudorandom sampling of NP-witnesses: given a Boolean circuit A, produce a polynomial-size sample space that is computationally indistinguishable from the uniform distribution over A/sup -1/(1).  also present applications. For example,  observe that Cai's proof that S/sub 2//sup p/ /spl sube/ ZPP/sup NP/ and the learning algorithm of Bshouty et al. can be seen as reductions to sampling that are not probabilistic. As a consequence they can be derandomized under the assumption stated above, which is aker than the assumption that was previously known to suffice."}]