We used the dynamical language approach for Datasets 1 and 2 in [5] and Dataset 3 in [32] . Some biological comparisons of this approach with the Markov model approach on Datasets 1 and 2 were given in [5] . Recently we found that wrong data of the Archaea Crenarchaeota bacterium Pyrobaculum aerophilum (Pyrae) from Dataset 1 was used in [5] . Using the right genome data, Pyrobaculum aerophilum (Pyrae) groups with the other Archaea Crenarchaeota bacteria correctly (when we use the amino acid sequences of all protein-coding genes from genomes and K = 6). After this correction, the resulting tree is better than the one in [11] from the biological point of view, with all firmicutes group together and the other branches are similar. For Dataset 2, we obtained two trees with the same topology to those using the dynamical language approach in [5] and the Markov model approach in [12] (also using the amino acid sequences of all protein-coding genes from genomes and K = 6). For Dataset 3, we reported in [32] a good tree in agreement with the current understanding of the phylogeny of vertebrates revealed by the traditional approaches using the dynamical language approach (based on the whole DNA sequences of genomes and K = 11). This tree is better than the one in [19] and the one obtained by the Markov model approach. Hence we just need to compare the best trees obtained by the dynamical language approach using the two proper distance metrics with the best trees obtained from the pseudo-distance in [5] based on the first three datasets. In 2009, Guyon et al. [31] compared four alignment free string distances for complete genome phylogeny using Dataset 4. We will compare our method in this paper with the results in [31] based on Dataset 4.