On the Approximation of the Kolmogorov Complexity for DNA Sequences

  • Diogo PratasEmail author
  • Armando J. Pinho
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10255)


The Kolmogorov complexity furnishes several ways for studying different natural processes that can be expressed using sequences of symbols from a finite alphabet, such as the case of DNA sequences. Although the Kolmogorov complexity is not algorithmically computable, it can be approximated by lossless normal compressors. In this paper, we use a specific DNA compressor to approximate the Kolmogorov complexity and we assess it regarding its normality. Then, we use it on several datasets, that are constituted by different DNA sequences, representing complete genomes of different species and domains. We show several evolution-related insights associated with the complexity, namely that, globally, archaea have higher relative complexity than bacteria and eukaryotes.


Kolmogorov complexity Compression DNA sequences 



This work was partially funded by FEDER (Programa Operacional Factores de Competitividade - COMPETE) and by National Funds through the FCT - Foundation for Science and Technology, in the context of the projects UID/CEC/00127/2013, PTCD/EEI-SII/6608/2014.


  1. 1.
    Kolmogorov, A.N.: Three approaches to the quantittative definition of information. Probl. Inf. Transm. 1(1), 1–7 (1965)MathSciNetGoogle Scholar
  2. 2.
    Solomonoff, R.J.: A formal theory of inductive inference: Part I. Inf. Control 7(1), 1–22 (1964)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Solomonoff, R.J.: A formal theory of inductive inference: Part II. Inf. Control 7(2), 224–254 (1964)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chaitin, G.J.: On the length of programs for computing finite binary sequences. J. ACM 13, 547–569 (1966)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Wallace, C.S., Boulton, D.M.: An information measure for classification. Comput. J. 11(2), 185–194 (1968)CrossRefzbMATHGoogle Scholar
  6. 6.
    Rissanen, J.: Modeling by shortest data description. Automatica 14, 465–471 (1978)CrossRefzbMATHGoogle Scholar
  7. 7.
    Hutter, M.: Algorithmic information theory: a brief non-technical guide to the field. Scholarpedia 9620, March 2007Google Scholar
  8. 8.
    Li, M., Vitányi, P.: An Introduction to Kolmogorov Complexity and Its Applications, 3rd edn. Springer, Heidelberg (2008)CrossRefzbMATHGoogle Scholar
  9. 9.
    Turing, A.: On computable numbers, with an application to the Entscheidungs problem. Proc. Lond. Math. Soc. 42(2), 230–265 (1936)zbMATHGoogle Scholar
  10. 10.
    Cilibrasi, R., Vitányi, P.M.B.: Clustering by compression. IEEE Trans. Inf. Theor. 51(4), 1523–1545 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hammer, D., Romashchenko, A., Shen, A., Vereshchagin, N.: Inequalities for Shannon entropy and Kolmogorov complexity. J. Comput. Syst. Sci. 60(2), 442–464 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Cebrián, M., Alfonseca, M., Ortega, A.: Common pitfalls using the normalized compression distance: what to watch out for in a compressor. Commun. Inf. Syst. 5(4), 367–384 (2005)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Pratas, D., Pinho, A.J., Ferreira, P.: Efficient compression of genomic sequences. In: Proceedings of the Data Compression Conference, DCC-2016, Snowbird, UT, pp. 231–240, March 2016Google Scholar
  14. 14.
    Pratas, D.: Compression and analysis of genomic data. Ph.D. thesis, University of Aveiro (2016)Google Scholar
  15. 15.
    Hosseini, M., Pratas, D., Pinho, A.J.: A survey on data compression methods for biological sequences. Information 7(4), 56 (2016)CrossRefGoogle Scholar
  16. 16.
    Bywater, R.P.: Prediction of protein structural features from sequence data based on Shannon entropy and Kolmogorov complexity. PLoS ONE 10(4), e0119306 (2015)CrossRefGoogle Scholar
  17. 17.
    Ferreira, P.J.S.G., Pinho, A.J.: Compression-based normal similarity measures for DNA sequences. In: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-2014, Florence, Italy, pp. 419–423, May 2014Google Scholar
  18. 18.
    Pratas, D., Pinho, A.J., Rodrigues, J.M.O.S.: XS: a FASTQ read simulator. BMC Res. Notes 7(1), 40 (2014)CrossRefGoogle Scholar
  19. 19.
    Hedges, S.B.: The origin and evolution of model organisms. Nat. Rev. Genet. 3(11), 838–849 (2002)CrossRefGoogle Scholar
  20. 20.
    Parfrey, L.W., Grant, J., Tekle, Y.I., Lasek-Nesselquist, E., Morrison, H.G., Sogin, M.L., Patterson, D.J., Katz, L.A.: Broadly sampled multigene analyses yield a well-resolved eukaryotic tree of life. Syst. Biol. 59(5), 518–533 (2010)CrossRefGoogle Scholar
  21. 21.
    Podani, J., Oltvai, Z.N., Jeong, H., Tombor, B., Barabási, A.L., Szathmary, E.: Comparable system-level organization of archaea and eukaryotes. Nat. Genet. 29(1), 54–56 (2001)CrossRefGoogle Scholar
  22. 22.
    Wu, D., Hugenholtz, P., Mavromatis, K., Pukall, R., Dalin, E., Ivanova, N.N., Kunin, V., Goodwin, L., Wu, M., Tindall, B.J., et al.: A phylogeny-driven genomic encyclopaedia of bacteria and archaea. Nature 462(7276), 1056–1060 (2009)CrossRefGoogle Scholar
  23. 23.
    Koonin, E.V., Senkevich, T.G., Dolja, V.V.: The ancient virus world and evolution of cells. Biol. Direct 1(1), 29 (2006)CrossRefGoogle Scholar
  24. 24.
    Maumus, F., Epert, A., Nogué, F., Blanc, G.: Plant genomes enclose footprints of past infections by giant virus relatives. Nat. Commun. 5, 4268 (2014)Google Scholar
  25. 25.
    Filée, J.: Multiple occurrences of giant virus core genes acquired by eukaryotic genomes: the visible part of the iceberg? Virology 466, 53–59 (2014)CrossRefGoogle Scholar
  26. 26.
    Colson, P., De Lamballerie, X., Yutin, N., Asgari, S., Bigot, Y., Bideshi, D.K., Cheng, X.W., Federici, B.A., Van Etten, J.L., Koonin, E.V., et al.: “Megavirales”, a proposed new order for eukaryotic nucleocytoplasmic large DNA viruses. Arch. Virol. 158(12), 2517–2521 (2013)CrossRefGoogle Scholar
  27. 27.
    Forterre, P., Krupovic, M., Prangishvili, D.: Cellular domains and viral lineages. Trends Microbiol. 22(10), 554–558 (2014)CrossRefGoogle Scholar
  28. 28.
    Pennisi, E.: Ever-bigger viruses shake tree of life. Science 341(6143), 226–227 (2013)CrossRefGoogle Scholar
  29. 29.
    Canchaya, C., Fournous, G., Chibani-Chennoufi, S., Dillmann, M.L., Brüssow, H.: Phage as agents of lateral gene transfer. Curr. Opin. Microbiol. 6(4), 417–424 (2003)CrossRefGoogle Scholar
  30. 30.
    Bitra, K., Burke, G.R., Strand, M.R.: Permissiveness of lepidopteran hosts is linked to differential expression of bracovirus genes. Virology 492, 259–272 (2016)CrossRefGoogle Scholar
  31. 31.
    Pratas, D., Pinho, A.J.: Compressing the human genome using exclusively Markov models. In: Rocha, M.P., Rodríguez, J.M.C., Fdez-Riverola, F., Valencia, A. (eds.) PACBB 2011. AISC, vol. 93, pp. 213–220. Springer, Heidelberg (2011)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.IEETAUniversity of AveiroAveiroPortugal

Personalised recommendations