BPP的伪随机oracle表征

[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI:10.1109/SCT.1991.160261

J. H. Lutz

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引用次数: 21

摘要

C.H. Bennett和J. Gill(1981)和K. Ambos-Spies(1986)的研究表明，以下条件是等价的:(i)在BPP中为L;(二);对于几乎所有的神谕A, l在P/sup A/。这里证明了下列条件也等价于(i)和(ii):(iii) P/sup A/中的L具有P空间测度1的神谕集合A;(iv)对于P/sup A/中的每个pspace-random oracle A, L。从这个特征可以得出，DSPACE (2/sup poly/)中的几乎每个A对于BPP来说都是多项式时间困难的。简而言之，证明的主要内容是相对于每个伪随机预言存在伪随机生成器。

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A pseudorandom oracle characterization of BPP

It is known from work of C.H. Bennett and J. Gill (1981) and K. Ambos-Spies (1986) that the following conditions are equivalent: (i) L in BPP; (ii); for almost all oracles A, l in P/sup A/. It is shown here that the following conditions are also equivalent to (i) and (ii): (iii) the set of oracles A for which L in P/sup A/ has pspace-measure 1; (iv) for every pspace-random oracle A, L in P/sup A/. It follows from this characterization that almost every A in DSPACE (2/sup poly/) is polynomial-time hard for BPP. Succinctly, the main content of the proof is that pseudorandom generators exist relative to every pseudorandom oracle.<>

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[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference

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