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Duplication Grammars
Carlos MARTÍN-VIDE 3, Gheorghe P AUN 4
Abstract
Motivated by the abundance of duplication operations appearing in natural languages and in the genetic area, we introduce a generative mechanism based on duplication operations: one starts from a given finite set of strings and one produces new strings by copying certain substrings, according to a set of given rules (which specify contexts where duplicated substrings can be inserted). We mainly investigate the power of such devices, comparing the obtained families of languages to each other and with families in the Chomsky hierarchy. In this context, we also solve a problem left open in a paper by Dassow and Mitrana, [], even giving a stronger results: the iterated duplication with rules of only one type (see formal definitions in the sequel) can generate non-context-free languages (even non-matrix languages).
Footnotes:
1 Research supported by the Direcció General de Recerca, Generalitat de Catalunya (PIV)
2 Research supported by the Direcció General de Recerca, Generalitat de Catalunya (PIV)
3 Research Group in Mathematical Linguistics and Language Engineering Rovira i Virgili University Pl. Imperial T\` arraco 1, 43005 Tarragona, Spain e-mail: cmv@astor.urv.es
4 Institute of Mathematics of the Romanian Academy PO Box 1 - 764, 70700 Bucure sti, Romania, e-mail: gpaun@imar.ro.