Synchronized Shuffle on Backbones

Issue title: SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu

Article type: Research Article

Authors: Manea, Florin | Mitrana, Victor | Voinescu, Daniel-Claudian

Affiliations: Faculty of Mathematics and Computer Science University of Bucharest Str. Academiei 14, Bucharest, Romania. E-mails: [email protected]; [email protected]; [email protected]

Abstract: In this paper we continue the study on synchronized shuffle started in [5] by introducing the condition that the two words which are to be shuffled have to synchronize on a predefined set of backbones. As far as the language-theoretic properties of this operation are concerned, we prove that in a trio the closure under shuffle is equivalent to the closure under synchronized shuffle on a regular set of backbones. Based on this result we show that a set of backbones is regular if and only if the synchronized shuffle of every two regular languages on that set is also regular. Some relationships between this operation and the synchronized shuffle operations introduced in [5] are presented and some open problem are finally discussed.

Keywords: Shuffle, synchronized shuffle, backbone, synchronized shuffle on backbones, formal languages

Journal: Fundamenta Informaticae, vol. 73, no. 1-2, pp. 191-202, 2006