Iterated TGR Languages: Membership Problem and Effective Closure Properties

  • Ian McQuillan
  • Kai Salomaa
  • Mark Daley
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)


We show that membership is decidable for languages defined by iterated template-guided recombination systems when the set of templates is regular and the initial language is context-free. Using this result we show that when the set of templates is regular and the initial language is context-free (respectively, regular) we can effectively construct a pushdown automaton (respectively, finite automaton) for the corresponding iterated template-guided recombination language.


Turing Machine Regular Language Closure Property Membership Problem Pushdown Automaton 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aho, A.V.: Indexed grammars – an extenion of context-free grammars. Journal of the ACM 15, 647–671 (1968)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Daley, M., Ibarra, O., Kari, L., McQuillan, I., Nakano, K.: Closure and decision properties of some language classes under ld and dlad bio-operations. J. Automata, Languages and Combinatorics 8, 477–498 (2003)MATHMathSciNetGoogle Scholar
  3. 3.
    Daley, M., McQuillan, I.: Template-guided DNA recombination. Theoret. Comput. Sci. 330, 237–250 (2005)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Daley, M., McQuillan, I.: Useful templates and iterated template-guided DNA recombination in ciliates. Theory of Computing Systems (in press). E-print available doi: 10.1007/s00224-005-1206-6Google Scholar
  5. 5.
    Eilenberg, S.: Automata, Languages, and Machines, vol. A. Academic Press Inc., New York (1974)MATHGoogle Scholar
  6. 6.
    Engelfriet, J.: Iterated stack automata and complexity classes. Information and Computation 95, 21–75 (1991)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Ginsburg, S.: Algebraic and Automata-Theoretic Properties of Formal Languages. North-Holland, Amsterdam (1975)MATHGoogle Scholar
  8. 8.
    Head, T., Pixton, D.: Splicing and regularity (to appear), available at:
  9. 9.
    McQuillan, I., Salomaa, K., Daley, M.: Iterated TGR languages: Membership problem and effective closure properties. Queen’s School of Computing Technical Report No. 2006-513, available at:
  10. 10.
    Prescott, D.M.: Genome Gymnastics: Unique modes of DNA evolution and processing in ciliates. Nature Reviews Genetics 1, 191–198 (2000)CrossRefGoogle Scholar
  11. 11.
    Prescott, D.M., Ehrenfeucht, A., Rozenberg, G.: Template guided recombination for IES elimination and unscrambling of genes in stichotrichous ciliates. J. Theoretical Biology 222, 323–330 (2003)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 1–3. Springer, Heidelberg (1997)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ian McQuillan
    • 1
  • Kai Salomaa
    • 2
  • Mark Daley
    • 3
  1. 1.Department of Computer ScienceUniversity of SaskatchewanSaskatoonCanada
  2. 2.School of ComputingQueen’s UniversityKingstonCanada
  3. 3.Department of Computer Science and Department of BiologyUniversity of Western OntarioLondonCanada

Personalised recommendations