TY - GEN

T1 - Representations and characterizations of languages in chomsky hierarchy by means of insertion-deletion systems

AU - Pǎun, Gheorghe

AU - Pérez-Jiménez, Mario J.

AU - Yokomori, Takashi

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Context-free languages

KW - Insertion-deletion systems

KW - Recursively enumerable languages

KW - Regular languages

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M3 - Conference contribution

AN - SCOPUS:84905842130

SN - 9788070976883

T3 - Descriptional Complexity of Formal Systems - 9th International Workshop, DCFS 2007

SP - 129

EP - 140

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

PB - Technical University of Kosice

T2 - 9th International Workshop on Descriptional Complexity of Formal Systems, DCFS 2007

Y2 - 20 July 2007 through 22 July 2007

ER -