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Context Insertions

  • Paolo Bottoni
  • Radu Gramatovici
  • Anna Labella
  • Florin Manea
  • Victor Mitrana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6610)

Abstract

In this paper we consider an operation of inserting contexts in a word controlled by a contextual scheme X which provides a selection criterion for contextual insertion. We say that a language L is k-stable w.r.t. a contextual scheme X if by making any k context insertions in a word of L we still obtain a word of L; L is k-anti-stable w.r.t. X if by making any k context insertions in a word of L we get a word not in L; L is called k-error-correctable w.r.t. X if by making any k context insertions in a word x of L we get either a word in L or a word not in L which cannot be also obtained by making k context insertions in a word z of L different from x. We prove that all these properties are decidable for regular languages. We then define a distance between two words that measures the minimal number of context insertions in one of the words in order to obtain the other. Some properties of this distance, which is actually a semimetric, are investigated.

Keywords

Regular Language Plain Text Empty Word Input Word Formal Language Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Dieffenbach, C.W., Dveksler, G.S. (eds.): A Laboratory Manual. Cold Spring Harbor Laboratory Press (1995)Google Scholar
  2. 2.
    Kari, L., Thierrin, G.: Contextual Insertions/Deletions and Computability. Information and Computation 131, 47–61 (1996)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Karlin, S., Mocarski, E.S., Schachtel, G.A.: Molecular Evolution of Herpesviruses: Genomic and Protein Comparisons. J. of Virology 68, 1886–1902 (1994)Google Scholar
  4. 4.
    van Lindt, J.H.: Introduction to Coding Theory. Springer, Berlin (1982)Google Scholar
  5. 5.
    Marcus, S.: Contextual Grammars. Rev. Roum. Math. Pures Appl. 14, 1525–1534 (1969)MathSciNetMATHGoogle Scholar
  6. 6.
    Marcus, S.: Contextual Grammars and Natural Languages. In: Rozenberg, G., Salomaa, A. (eds.) The Handbook of Formal Languages, pp. 215–235. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  7. 7.
    Mateescu, A., Salomaa, A., Salomaa, K., Yu, S.: Lexical Analysis With Simple Finite-Fuzzy-Automaton Model. J. Universal Computer Science 1, 288–307 (1996)MATHGoogle Scholar
  8. 8.
    McGeoch, D.J.: Molecular Evolution of Large DNA Viruses of Eukaryotes. Seminars in Virology 3, 399–408 (1992)Google Scholar
  9. 9.
    Mitrana, V.: Contextual Insertion and Deletion. In: Păun, G. (ed.) Mathematical Linguistics and Related Topics, pp. 271–278. The Publishing House of the Romanian Academy (1994)Google Scholar
  10. 10.
    Oflezer, K.: Error-Tolerant Finite State Recognition. In: Proceedings of the Fourth International Workshop on Parsing Technologies, Prague, pp. 196–207 (September 20-24, 1995)Google Scholar
  11. 11.
    Păun, G.: Marcus Contextual Grammars. Kluwer, Dordrecht (1997)CrossRefMATHGoogle Scholar
  12. 12.
    Rozenberg, G., Salomaa, A. (eds.): The Handbook of Formal Languages. Springer, Heidelberg (1997)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Paolo Bottoni
    • 1
  • Radu Gramatovici
    • 2
  • Anna Labella
    • 1
  • Florin Manea
    • 2
    • 3
  • Victor Mitrana
    • 2
    • 4
  1. 1.Department of Computer Science“Sapienza” University of RomeRomeItaly
  2. 2.Faculty of Mathematics and Computer ScienceUniversity of BucharestBucharestRomania
  3. 3.Faculty of Computer ScienceOtto-von-Guericke UniversityMagdeburgGermany
  4. 4.Depto. Organización y Estructura de la InformaciónUniversidad Politécnica de MadridMadridSpain

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