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On the star-height of subword counting languages and their relationship to Rees zero-matrix semigroups

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Bourne_2016_Semigroups_TheoreticalCompSci_AAM.pdf (296.2Kb)
Date
15/11/2016
Author
Bourne, Tom
Ruškuc, Nik
Keywords
Regular language
Star-height
Subword
Rees matrix semigroup
QA75 Electronic computers. Computer science
T-NDAS
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Abstract
Given a word w over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in which w occurs as a contiguous subword modulo a fixed number, and prove that in each case it is at most one. We use these combinatorial results to show that any language recognised by a Rees (zero-)matrix semigroup over an abelian group is of generalised star-height at most one.
Citation
Bourne , T & Ruškuc , N 2016 , ' On the star-height of subword counting languages and their relationship to Rees zero-matrix semigroups ' , Theoretical Computer Science , vol. 653 , pp. 87-96 . https://doi.org/10.1016/j.tcs.2016.09.024
Publication
Theoretical Computer Science
Status
Peer reviewed
DOI
https://doi.org/10.1016/j.tcs.2016.09.024
ISSN
0304-3975
Type
Journal article
Rights
© 2016, Elsevier. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.sciencedirect.com / https://dx.doi.org/10.1016/j.tcs.2016.09.024
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/11811

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