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Omega-rational expressions with bounded synchronization delay

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journal contribution
posted on 23.02.2018, 09:29 by Volker Diekert, Manfred Kufleitner
© 2013, Springer Science+Business Media New York. In 1965 Sch ̈utzenberger published his famous result that star-free languages (SF) and aperiodic languages (AP) coincide over finite words, often written as SF = AP. Perrin generalized SF = AP to infinite words in the mid 1980s. In 1973 Sch ̈utzenberger presented another (and less known) characteri- zation of aperiodic languages in terms of rational expressions where the use of the star operation is restricted to prefix codes with bounded synchronization delay and no complementation is used. We denote this class of languages by SD. In this paper, we present a generalization of SD = AP to infinite words. This became possible via a substantial simplification of the proof for the cor- responding result for finite words. Moreover, we show that SD = AP can be viewed as more fundamental than SF = AP in the sense that the classical 1965 result of Sch ̈utzenberger and its 1980s extension to infinite words by Perrin are immediate consequences of SD = AP.

Funding

M.K. was supported by the German Research Foundation (DFG) under grant DI 435/5-1 and by ANR 2010 BLAN 0202 FREC.

History

School

  • Science

Department

  • Computer Science

Published in

Theory of Computing Systems

Volume

56

Issue

4

Pages

686 - 696

Citation

DIEKERT, V. and KUFLEITNER, M., 2015. Omega-rational expressions with bounded synchronization delay. Theory of Computing Systems, 56(4), pp. 686-696.

Publisher

© Springer

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2015

Notes

This is a post-peer-review, pre-copyedit version of an article published in Theory of Computing Systems. The final authenticated version is available online at: https://doi.org/10.1007/s00224-013-9526-4

ISSN

1432-4350

eISSN

1433-0490

Language

en