An optimized direct algorithm to estimate the Kolmogorov entropy from a time series

The computation of the Kolmogorov entropy from a time series with a direct method involves the evaluation of the probabilities of the box sequences in the phase-space. This approach leads to a particular string matching problem. In this work an optimized algorithm is presented for the efficient computation of various estimates K_l of the Kolmogorov entropy, each obtained with a different length l of the box sequence, from l = 2 up to l_max.