Mathematica Slovaca

, Volume 64, Issue 1, pp 229–246

Some considerations on Hydra groups and a new bound for the length of words

  • Daniele Ettore Otera
  • Francesco G. Russo
  • Vincenzo Russo


After a survey on some recent results of Riley and others on Ackermann functions and Hydra groups, we make an analogy between DNA sequences, whose growth is the same of that of Hydra groups, and a musical piece, written with the same algorithmic criterion. This is mainly an aesthetic observation, which emphasizes the importance of the combinatorics of words in two different contexts. A result of specific mathematical interest is placed at the end, where we sharpen some previous bounds on deterministic finite automata in which there are languages with hairpins.


isoperimetric functions finitely presented groups lengths of words counterpoint Myhill-Nerode’s theorem 

2010 Mathematics Subject Classification

Primary 57M50 Secondary 68R05, 68Q15 


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Copyright information

© Versita Warsaw and Springer-Verlag Wien 2014

Authors and Affiliations

  • Daniele Ettore Otera
    • 1
    • 2
  • Francesco G. Russo
    • 3
    • 4
  • Vincenzo Russo
    • 5
  1. 1.Laboratoire de Mathématiques Bâtiment 425Faculté de Science d’Orsay, Université Paris-Sud 11Orsay CedexFrance
  2. 2.Institute of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  3. 3.DEIMUniversitá degli Studi di PalermoPalermoItaly
  4. 4.Instituto de MatemáticaUniversidade Federal do Rio de Janeiro, Ilha do FundãoRio de JaneiroBrazil
  5. 5.Dipartimento di EmatologiaUniversitá degli Studi di Napoli Federico IINaplesItaly

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