We characterize the algorithmic dimensions (i.e., the lower and upper asymptotic densities of information) of infinite binary sequences in terms of the inability of learning functions having an algorithmic constraint to detect patterns in them. Our pattern detection criterion is a quantitative extension of the criterion that Zaffora Blando used to characterize the algorithmically random (i.e., Martin-L\"of random) sequences. Our proof uses Lutz's and Mayordomo's respective characterizations of algorithmic dimension in terms of gales and Kolmogorov complexity.

翻译：我们通过具有算法约束的学习函数无法检测无限二进制序列中的模式，来刻画这些序列的算法维度（即信息的下渐近密度和上渐近密度）。我们的模式检测准则是Zaffora Blando用于刻画算法随机（即Martin-Löf随机）序列准则的定量扩展。我们的证明利用了Lutz和Mayordomo分别基于赌金过程与柯尔莫哥洛夫复杂度对算法维度的刻画。