Pseudorandom Generators, Typically-Correct Derandomization, and Circuit Lower Bounds
Pseudorandom Generators, Typically-Correct Derandomization, and Circuit Lower Bounds
复制标题
伪随机发生器、典型正确的去随机化和电路下界
DOI：
10.1007/s00037-011-0019-z
复制
发表时间：
2011
影响因子：
1.4
通讯作者：
Ronen Shaltiel
中科院分区：
文献类型：
--
作者：
Jeff Kinne;D. Melkebeek;Ronen Shaltiel
在各种算法设置中，derandomization的区域试图提供有效的确定性模拟。研究首先，我们开发了一种基于种子延伸的伪和生成器来构建典型的降低构态的通用方法，这些伪随身杂音是伪随机的生成器，我们使用我们的种子来获得条件和无条件的差异。我们的技术表明，我们的技术严格通过shaltiel概括了基于随机性的提取器，并简化了一些已知结果的证据。典型的bpp中的多项式仿真基于（看似）比早期工作中所使用的硬度较弱Kabanets和Impagliazzo的工作对零错误，我们在Goldreich和Wigderson考虑的范围内建立了一个积极的答案。原始的，不依赖于Impagliazzo，Kabanets和Wigderson的结果，即具有多项式尺寸电路的NEXP意味着NEXP与EXP一致。
The area of derandomization attempts to provide efficient deterministic simulations of randomized algorithms in various algorithmic settings. Goldreich and Wigderson introduced a notion of “typically-correct” deterministic simulations, which are allowed to err on few inputs. In this paper, we further the study of typically-correct derandomization in two ways. First, we develop a generic approach for constructing typically-correct derandomizations based on seed-extending pseudorandom generators, which are pseudorandom generators that reveal their seed. We use our approach to obtain both conditional and unconditional typically-correct derandomization results in various algorithmic settings. We show that our technique strictly generalizes an earlier approach by Shaltiel based on randomness extractors and simplifies the proofs of some known results. We also demonstrate that our approach is applicable in algorithmic settings where earlier work did not apply. For example, we present a typically-correct polynomial-time simulation for every language in BPP based on a hardness assumption that is (seemingly) weaker than the ones used in earlier work. Second, we investigate whether typically-correct derandomization of BPP implies circuit lower bounds. Extending the work of Kabanets and Impagliazzo for the zero-error case, we establish a positive answer for error rates in the range considered by Goldreich and Wigderson. In doing so, we provide a simpler proof of the zero-error result. Our proof scales better than the original one and does not rely on the result by Impagliazzo, Kabanets, and Wigderson that NEXP having polynomialsize circuits implies that NEXP coincides with EXP.