Arranging the bits of a random string or real into k columns of a two-dimensional array or higher dimensional structure is typically accompanied with loss in the Kolmogorov complexity of the columns, which depends on k. We quantify and characterize this phenomenon for arrays and trees and its relationship to negligible classes.
翻译:将随机字符串或实数的比特排列成二维数组或更高维结构的k列时,通常会导致各列Kolmogorov复杂度的损失,这种损失取决于k。我们针对数组和树结构量化并刻画了该现象及其与可忽略类的关系。