Morphic characterizations of language families in terms of insertion systems and star languages

Fumiya Okubo, Takashi Yokomori*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Insertion systems have a unique feature in that only string insertions are allowed, which is in marked contrast to a variety of the conventional computing devices based on string rewriting. This paper will mainly focus on those systems whose insertion operations are performed in a context-free fashion, called context-free insertion systems, and obtain several characterizations of language families with the help of other primitive languages (like star languages) as well as simple operations (like projections, weak-codings). For each k < 1, a language L is a k-star language if L = F+ for some finite set F with the length of each string in F is no more than k. The results of this kind have already been presented in [10] by Pun et al., while the purpose of this paper is to prove enhanced versions of them. Specifically, we show that each context-free language L can be represented in the form L = h(L(γ) ∩F+), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context-free manner), h is a projection, and F+ is a 2-star language. A similar characterization can be obtained for recursively enumerable languages, where insertion systems of weight (3, 3) and 2-star languages are involved.

Original languageEnglish
Pages (from-to)247-260
Number of pages14
JournalInternational Journal of Foundations of Computer Science
Issue number1
Publication statusPublished - 2011 Jan


  • Insertion systems
  • Morphic characterization
  • Star languages

ASJC Scopus subject areas

  • Computer Science (miscellaneous)


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