Large Alphabets and Incompressibility

Details Large Alphabets and Incompressibility Large Alphabets and Incompressibility

2005-06-14

arxiv.org/abs/cs/0506056v3

Computer Science

Information Theory

Scientific paper

10.1016/j.ipl.2006.04.008

We briefly survey some concepts related to empirical entropy -- normal numbers, de Bruijn sequences and Markov processes -- and investigate how well it approximates Kolmogorov complexity. Our results suggest $\ell$th-order empirical entropy stops being a reasonable complexity metric for almost all strings of length $m$ over alphabets of size $n$ about when $n^\ell$ surpasses $m$.

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