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)


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.


Regular Language Plain Text Empty Word Input Word Formal Language Theory 
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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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