Abstract:
This report compares a variety of computable information measures for finite strings. These include
Shannon’s n-block entropy, the three best known versions of the Lempel-Ziv production complexity
(LZ-76, LZ-77, and LZ-78), and the lesser known T-entropy. We apply these measures to strings of
known entropy, each derived from the logistic map. Pesin’s identity allows us to deduce corresponding
Shannon entropies (Kolmogorov-Sinai entropies) for the sample strings, without resorting to probabilistic
methods.
