Omega-rational expressions with bounded synchronization delay
journal contributionposted on 2018-02-23, 09:29 authored 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.
M.K. was supported by the German Research Foundation (DFG) under grant DI 435/5-1 and by ANR 2010 BLAN 0202 FREC.
- Computer Science
Published inTheory of Computing Systems
Pages686 - 696
CitationDIEKERT, V. and KUFLEITNER, M., 2015. Omega-rational expressions with bounded synchronization delay. Theory of Computing Systems, 56(4), pp. 686-696.
- AM (Accepted Manuscript)
Publisher statementThis 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/
NotesThis 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