Hairpin Finite Automata

  • Henning Bordihn
  • Markus Holzer
  • Martin Kutrib
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4588)


We introduce and investigate nondeterministic finite automata with the additional ability to apply the hairpin inversion operation to the remaining part of the input. We consider three different modes of hairpin operations, namely left-most hairpin, general hairpin, and right-most hairpin. We show that these operations do not increase the computation power, when the number of operations is bounded by a constant. An unbounded number of these operations leads to language families that are properly contained in the family of context-sensitive languages and are supersets of the family of regular languages. Moreover, we show that in most cases we obtain incomparability results for the language families under consideration. Finally, we summarize closure properties of language families accepted by variants of hairpin finite automata.


Turing Machine Regular Language Closure Property Input Symbol State Automaton 
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  1. 1.
    Adleman, L.: Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Bordihn, H., Holzer, M., Kutrib, M.: Input reversals and iterated pushdown automata—a new characterization of Khabbaz geometric hierarchy of languages. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds.) DLT 2004. LNCS, vol. 3340, pp. 102–113. Springer, Heidelberg (2004)Google Scholar
  3. 3.
    Bordihn, H., Holzer, M., Kutrib, M.: Revolving-input finite automata. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 168–179. Springer, Heidelberg (2005)Google Scholar
  4. 4.
    Daley, M., Ibarra, O., Kari, L.: Closure properties and decision questions of some language classes under ciliate bio-operations. Theoretical Computer Science 306, 19–38 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Daley, M., Kari, L., McQuillan, I.: Families of languages defined by ciliate bio-operations. Theoretical Computer Science 320, 51–69 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Dassow, J., Holzer, M.: Language families defined by a ciliate bio-operation: Hierarchies and decision problems. International Journal of Foundations of Computer Science 16, 645–662 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Dassow, J., Mitrana, V., Salomaa, A.: Operations and language generating devices suggested by genome evolution. Theoretical Computer Science 270, 701–738 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Dassow, J., Păun, G.: Remarks on operations suggested by mutations in genomes. Fundamenta Informaticae 36, 183–200 (1998)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Ehrenfeucht, A., Prescott, D.M., Rozenberg, G.: Computational aspects of gene (un)scrambling in ciliates. In: Landweber, L.F., Winfree, E. (eds.) Evolution as Computation, pp. 45–86. Springer, Heidelberg (2001)Google Scholar
  10. 10.
    Holzer, M., Kutrib, M.: Flip-pushdown automata: k + 1 pushdown reversals are better than k. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 490–501. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Kari, L., Landweber, L.F.: Computational power of gene rearrangement. In: Winfree, E., Gifford, D. (eds.) DNA Based Computers V, DIMACS 54, pp. 207–216 (2000)Google Scholar
  12. 12.
    Prescott, D.M.: Cutting, slicing, reordering, and elimination of DNA sequences in hypotrichous ciliates. BioEssays 14, 317–324 (1992)CrossRefGoogle Scholar
  13. 13.
    Prescott, D.M.: Genome gymnastics: Unique modes of DNA evolution and processing in ciliates. Nature Review Genetics 1, 191–198 (2000)CrossRefGoogle Scholar
  14. 14.
    Sarkar, P.: Pushdown automaton with the ability to flip its stack. Report TR01-081, Electronic Colloquium on Computational Complexity (ECCC) (November 2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Henning Bordihn
    • 1
  • Markus Holzer
    • 2
  • Martin Kutrib
    • 3
  1. 1.Institut für Informatik, Universität Potsdam, August-Bebel-Straße 89, D-14482 PotsdamGermany
  2. 2.Institut für Informatik, Technische Universität München, Boltzmannstraße 3, D-85748 Garching bei MünchenGermany
  3. 3.Institut für Informatik, Universität Giessen, Arndtstraße 2, D-35392 GiessenGermany

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