A Kolmogorov Complexity-based Genetic Programming Tool for String Compression

By following the guidelines set in one of our previous papers, in this paper we face the problem of Kolmogorov complexity-estimate for binary strings by making use of a Genetic Programming approach. This consists in evolving a population of Lisp programs looking for the "optimal" program that generates a given string. By taking into account several target binary strings belonging to different formal languages, we show the effectiveness of our approach in obtaining an approximation from the above of the Kolmogorov complexity function. Moreover, the adequate choice of "similar" target strings allows our system to show very interesting computational strategies. Experimental results indicate that our tool achieves promising compression rates for binary strings belonging to formal languages. Furthermore, even for more complicated strings our method can work, provided that some degree of loss is accepted. These results constitute a first step in using Kolmogorov complexity for string compression.