Representations and characterizations of languages in chomsky hierarchy by means of insertion-deletion systems

Gheorghe Pǎun, Mario J. Pérez-Jiménez, Takashi Yokomori

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability were obtained in this framework. In this note we contribute to this research direction with a new characterization of this type, as well as with representations of regular and context-free languages, mainly starting from context-free insertion systems of as small as possible complexity. For instance, each recursively enumerable language L can be represented in a way similar to the celebrated Chomsky-Scḧutzenberger representation of context-free languages, i.e., in the form L = h(L(γ) ∩D), where is an insertion system of weight (3, 0) (at most three symbols are inserted in a context of length zero), h is a projection, and D is a Dyck language. A similar representation can be obtained for regular languages, involving insertion systems of weight (2,0) and star languages, as well as for context-free languages - this time using insertion systems of weight (3, 0) and star languages.

Original languageEnglish
Title of host publicationDescriptional Complexity of Formal Systems - 9th International Workshop, DCFS 2007
PublisherTechnical University of Kosice
Pages129-140
Number of pages12
ISBN (Print)9788070976883
Publication statusPublished - 2007 Jan 1
Event9th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2007 - High Tatras, Slovakia
Duration: 2007 Jul 202007 Jul 22

Publication series

NameDescriptional Complexity of Formal Systems - 9th International Workshop, DCFS 2007

Conference

Conference9th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2007
CountrySlovakia
CityHigh Tatras
Period07/7/2007/7/22

Keywords

  • Context-free languages
  • Insertion-deletion systems
  • Recursively enumerable languages
  • Regular languages

ASJC Scopus subject areas

  • Software

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  • Cite this

    Pǎun, G., Pérez-Jiménez, M. J., & Yokomori, T. (2007). Representations and characterizations of languages in chomsky hierarchy by means of insertion-deletion systems. In Descriptional Complexity of Formal Systems - 9th International Workshop, DCFS 2007 (pp. 129-140). (Descriptional Complexity of Formal Systems - 9th International Workshop, DCFS 2007). Technical University of Kosice.