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

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

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability and characterizations or representations of languages in Chomsky hierarchy 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-Schützenberger representation of context-free languages, i.e., in the form L h(L(γ) ∩ D), where γ 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
Pages (from-to)859-871
Number of pages13
JournalInternational Journal of Foundations of Computer Science
Volume19
Issue number4
DOIs
Publication statusPublished - 2008 Aug 1

Keywords

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

ASJC Scopus subject areas

  • Computer Science (miscellaneous)

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