任意序列均可从随机序列解压缩
Every Sequence is Decompressible from a Random One
摘要：
Kucera和Gacs分别证明了每一个无穷序列都是图灵可约为马丁-洛夫随机序列的。这一结果是通过证明每一个无限序列S是图灵可约为马丁-洛夫随机序列R，使得计算S的n位所需的R的渐近位数除以n，正好是S的构造维数。它表明，这是查询位的最佳比例计算位实现图灵约简。作为这一结果的应用，给出了构造维数的图灵约化压缩比的一个新的刻画。
英文摘要：
Kucera and Gacs independently showed that every infinite sequence is Turing reducible to a Martin-Lof random sequence. This result is extended by showing that every infinite sequence S is Turing reducible to a Martin-Lof random sequence R such that the asymptotic number of bits of R needed to compute n bits of S, divided by n, is precisely the constructive dimension of S. It is shown that this is the optimal ratio of query bits to computed bits achievable with Turing reductions. As an application of this result, a new characterization of constructive dimension is given in terms of Turing reduction compression ratios.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
