Advertisement

Site-Directed Insertion: Decision Problems, Maximality and Minimality

  • Da-Jung Cho
  • Yo-Sub Han
  • Kai Salomaa
  • Taylor J. Smith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10952)

Abstract

Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider decision problems and language equations involving site-directed insertion. By relying on the tools provided by semantic shuffle on trajectories we show that one variable equations involving site-directed insertion and regular constants can be solved. We consider also maximal and minimal variants of the site-directed insertion operation.

References

  1. 1.
    Birget, J.C.: Intersection and union of regular languages and state complexity. Inf. Process. Lett. 43, 185–190 (1992)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cho, D.-J., Han, Y.-S., Ng, T., Salomaa, K.: Outfix-guided insertion. Theor. Comput. Sci. 701, 70–84 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Csuhaj-Varju, E., Petre, I., Vaszil, G.: Self-assembly of string and languages. Theor. Comput. Sci. 374, 74–81 (2007)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Daley, M., Kari, L., Gloor, G., Siromoney, R.: Circular contextual insertions/deletions with applications to biomolecular computation. In: String Processing and Information Retrieval Symposium, pp. 47–54 (1999)Google Scholar
  5. 5.
    Domaratzki, M.: Semantic shuffle on and deletion along trajectories. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds.) DLT 2004. LNCS, vol. 3340, pp. 163–174. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-30550-7_14CrossRefGoogle Scholar
  6. 6.
    Domaratzki, M.: Trajectory-based codes. Acta Inf. 40, 491–527 (2004)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Domaratzki, M., Rozenberg, G., Salomaa, K.: Interpreted trajectories. Fundamenta Informaticae 73, 81–97 (2006)MathSciNetMATHGoogle Scholar
  8. 8.
    Enaganti, S., Kari, L., Kopecki, S.: A formal language model of DNA polymerase enzymatic activity. Fundamenta Informaticae 138, 179–192 (2015)MathSciNetMATHGoogle Scholar
  9. 9.
    Enaganti, S., Ibarra, O., Kari, L., Kopecki, S.: On the overlap assembly of strings and languages. Nat. Comput. 16, 175–185 (2017)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Franco, G., Manca, V.: Algorithmic applications of XPCR. Nat. Comput. 10, 805–811 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Han, Y.-S., Ko, S.-K., Ng, T., Salomaa, K.: State complexity of insertion. Int. J. Found. Comput. Sci. 27, 863–878 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Holzer, M., Jakobi, S.: Descriptional complexity of chop operations on unary and finite languages. J. Autom. Lang. Comb. 17(2–4), 165–183 (2012)MathSciNetMATHGoogle Scholar
  13. 13.
    Holzer, M., Jakobi, S., Kutrib, M.: The chop of languages. Theor. Comput. Sci. 682, 122–137 (2017)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Jürgensen, H., Konstantinidis, S.: Codes. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, Vol. 1, pp. 511–607. Springer, Heidelberg (1997).  https://doi.org/10.1007/978-3-642-59136-5_8CrossRefGoogle Scholar
  15. 15.
    Kari, L.: On language equations with invertible operations. Theor. Comput. Sci. 132, 129–150 (1994)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Kari, L., Thierrin, G.: Contextual insertions/deletions and computability. Inf. Comput. 131, 47–61 (1996)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Mateescu, A., Rozenberg, G., Salomaa, A.: Shuffle on trajectories: syntactic constraints. Theor. Comput. Sci. 197, 1–56 (1998)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Reikofski, J., Yao, B.Y.: Polymerase chain reaction (PCR) techniques for site-directed mutagenesis. Biotechnol. Adv. 10, 535–547 (1992)CrossRefGoogle Scholar
  19. 19.
    Shallit, J.: A Second Course in Formal Languages and Automata Theory. Cambridge University Press, Cambridge (2009)MATHGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  • Da-Jung Cho
    • 1
  • Yo-Sub Han
    • 1
  • Kai Salomaa
    • 2
  • Taylor J. Smith
    • 2
  1. 1.Department of Computer ScienceYonsei UniversitySeoulRepublic of Korea
  2. 2.School of ComputingQueen’s UniversityKingstonCanada

Personalised recommendations