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Title: Omega-rational expressions with bounded synchronization delay
Authors: Diekert, Volker
Kufleitner, Manfred
Issue Date: 2015
Publisher: © Springer
Citation: DIEKERT, V. and KUFLEITNER, M., 2015. Omega-rational expressions with bounded synchronization delay. Theory of Computing Systems, 56(4), pp. 686-696.
Abstract: © 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.
Description: 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
Sponsor: M.K. was supported by the German Research Foundation (DFG) under grant DI 435/5-1 and by ANR 2010 BLAN 0202 FREC.
Version: Accepted for publication
DOI: 10.1007/s00224-013-9526-4
URI: https://dspace.lboro.ac.uk/2134/31969
Publisher Link: https://doi.org/10.1007/s00224-013-9526-4
ISSN: 1432-4350
Appears in Collections:Published Articles (Computer Science)

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