Outfix-Guided Insertion

(Extended Abstract)
  • Da-Jung Cho
  • Yo-Sub Han
  • Timothy Ng
  • Kai SalomaaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9840)


Motivated by work on bio-operations on DNA strings, we consider an outfix-guided insertion operation that can be viewed as a generalization of the overlap assembly operation on strings studied previously. As the main result we construct a finite language L such that the outfix-guided insertion closure of L is nonregular. We consider also the closure properties of regular and (deterministic) context-free languages under the outfix-guided insertion operation and decision problems related to outfix-guided insertion. Deciding whether a language recognized by a deterministic finite automaton is closed under outfix-guided insertion can be done in polynomial time.


Language operations Closure properties Regular languages 



Cho and Han were supported by the Basic Science Research Program through NRF funded by MEST (2015R1D1A1A01060097), the Yonsei University Future-leading Research Initiative of 2015 and the International Cooperation Program managed by NRF of Korea (2014K2A1A2048512). Ng and Salomaa were supported by Natural Sciences and Engineering Research Council of Canada Grant OGP0147224.


  1. 1.
    Bertram, J.S.: The molecular biology of cancer. Mol. Asp. Med. 21(6), 167–223 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Csuhaj-Varju, E., Petre, I., Vaszil, G.: Self-assembly of strings and languages. Theoret. Comput. Sci. 374, 74–81 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    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
  4. 4.
    Enaganti, S., Ibarra, O., Kari, L., Kopecki, S.: On the overlap assembly of strings and languages. Nat. Comput. (2016).
  5. 5.
    Enaganti, S.K., Ibarra, O.H., Kari, L., Kopecki, S.: Further remarks on DNA overlap assembly, manuscript (2016)Google Scholar
  6. 6.
    Enaganti, S.K., Kari, L., Kopecki, S.: A formal language model of dna polymerase enzymatic activity. Fundam. Inform. 138, 179–192 (2015)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Flavell, R., Sabo, D., Bandle, E., Weissmann, C.: Site-directed mutagenesis: effect of an extracistronic mutation on the in vitro propagation of bacteriophage qbeta RNA. Proc. Natl. Acad. Sci. 72(1), 367–371 (1975)CrossRefGoogle Scholar
  8. 8.
    Galiukschov, B.: Semicontextual grammars (in Russian). Mat. Log. Mat. Lingvistika 38–50 (1981)Google Scholar
  9. 9.
    Ginsburg, S., Greibach, S.: Deterministic context free languages. Inf. Control 9, 620–648 (1966)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Haussler, D.: Insertion languages. Inf. Sci. 31, 77–89 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hemsley, A., Arnheim, N., Toney, M.D., Cortopassi, G., Galas, D.J.: A simple method for site-directed mutagenesis using the polymerase chain reaction. Nucleic Acids Res. 17(16), 6545–6551 (1989)CrossRefGoogle Scholar
  12. 12.
    Kari, L.: On insertion and deletion in formal languages. Ph.D. thesis, University of Turku (1991)Google Scholar
  13. 13.
    Kari, L., Thierrin, G.: Contextual insertions/deletions and computability. Inf. Comput. 131(1), 47–61 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Krassovitskiy, A., Rogozhin, Y., Verlan, S.: Computational power of insertion-deletion (P) systems with rules of size two. Nat. Comput. 10, 835–852 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lee, J., Shin, M.K., Ryu, D.K., Kim, S., Ryu, W.S.: Insertion and deletion mutagenesis by overlap extension PCR. In: Braman, J. (ed.) In Vitro Mutagenesis Protocols, 3rd edn, pp. 137–146. Humana Press, New York (2010)CrossRefGoogle Scholar
  16. 16.
    Liu, H., Naismith, J.H.: An efficient one-step site-directed deletion, insertion, single and multiple-site plasmid mutagenesis protocol. BMC Biotechnol. 8(1), 91–101 (2008)CrossRefGoogle Scholar
  17. 17.
    Margenstern, M., Păun, G., Rogozhin, Y., Verlan, S.: Context-free insertion-deletion systems. Theoret. Comput. Sci. 330(2), 339–348 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Păun, G., Pérez-Jiménez, M.J., Yokomori, T.: Representations and characterizations of languages in Chomsky hierarchy by means of insertion-deletion systems. Int. J. Found. Comput. Sci. 19(4), 859–871 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Pǎun, G.: On semicontextual grammars. Bull. Math. Soc. Sci. Math. Rouman. 28, 63–68 (1984)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Shallit, J.: A Second Course in Formal Languages and Automata Theory. Cambridge University Press, Cambridge (2009)zbMATHGoogle Scholar
  21. 21.
    Takahara, A., Yokomori, T.: On the computational power of insertion-deletion systems. Nat. Comput. 2, 321–336 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Yu, S.: Regular languages. In: Salomaa, A., Rozenberg, G. (eds.) Handbook of Formal Languages, vol. I, pp. 41–110. Springer, Heidelberg (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Da-Jung Cho
    • 1
  • Yo-Sub Han
    • 1
  • Timothy Ng
    • 2
  • Kai Salomaa
    • 2
    Email author
  1. 1.Department of Computer ScienceYonsei UniversitySeoulRepublic of Korea
  2. 2.School of ComputingQueen’s UniversityKingstonCanada

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