二进制串长度中的线性项违反了在线决策复杂性的可加性
Additivity of on-line decision complexity is violated by a linear term in the length of a binary string
摘要:
我们表明,有无限多个二进制字符串z,这样的总和的预测偶数位的z给定的先前的不均匀位的在线决策复杂度,和预测的不均匀位的决策复杂度给定的先前的事件位,超过了z的柯尔莫哥洛夫复杂度的长度z的线性项。
英文摘要:
We show that there are infinitely many binary strings z, such that the sum of the on-line decision complexity of predicting the even bits of z given the previous uneven bits, and the decision complexity of predicting the uneven bits given the previous event bits, exceeds the Kolmogorov complexity of z by a linear term in the length of z.
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