Deterministic extractors for small-space sources
Deterministic extractors for small-space sources
复制标题
小空间源的确定性提取器
DOI：
10.1145/1132516.1132613
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
David Zuckerman
中科院分区：
文献类型：
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作者：
Jesse Kamp;Anup Rao;S. Vadhan;David Zuckerman
We give polynomial-time, deterministic randomness extractors for sources generated in small space, where we model space s sources on (0,1)n as sources generated by width 2s branching programs: For every constant δ>0, we can extract .99 δ n bits that are exponentially close to uniform (in variation distance) from space s sources of min-entropy δ n, where s=Ω(n). In addition, assuming an efficient deterministic algorithm for finding large primes, there是一个常数η> 0，因此，对于任何δ> n-η，我们可以从最小的空间源中提取M =（δ-δ）n位，以最小的空间源接近均匀，以前s =ω（β3n）（β3n），Δ≤1/2的模型，我们的结果是一个新的。独立来源和符号固定这些来源。
We give polynomial-time, deterministic randomness extractors for sources generated in small space, where we model space s sources on (0,1)n as sources generated by width 2s branching programs: For every constant δ>0, we can extract .99 δ n bits that are exponentially close to uniform (in variation distance) from space s sources of min-entropy δ n, where s=Ω(n). In addition, assuming an efficient deterministic algorithm for finding large primes, there is a constant η > 0 such that for any δ>n-η, we can extract m=(δ-δ)n bits that are exponentially close to uniform from space s sources with min-entropy δ n, where s=Ω(β3 n). Previously, nothing was known for δ ≤ 1/2, even for space 0.Our results are obtained by a reduction to a new class of sources that we call independent-symbol sources, which generalize both the well-studied models of independent sources and symbol-fixing sources. These sources consist of a string of n independent symbols over a d symbol alphabet with min-entropy k. We give deterministic extractors for such sources when k is as small as polylog(n), for small enough d.