### 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 language | English |
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Title of host publication | Descriptional Complexity of Formal Systems - 9th International Workshop, DCFS 2007 |

Publisher | Technical University of Kosice |

Pages | 129-140 |

Number of pages | 12 |

ISBN (Print) | 9788070976883 |

Publication status | Published - 2007 Jan 1 |

Event | 9th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2007 - High Tatras, Slovakia Duration: 2007 Jul 20 → 2007 Jul 22 |

### Publication series

Name | Descriptional Complexity of Formal Systems - 9th International Workshop, DCFS 2007 |
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### Conference

Conference | 9th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2007 |
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Country | Slovakia |

City | High Tatras |

Period | 07/7/20 → 07/7/22 |

### Keywords

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

### ASJC Scopus subject areas

- Software

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## Cite this

*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.