License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.129
URN: urn:nbn:de:0030-drops-62642
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6264/
Diekert, Volker ;
Walter, Tobias
Characterizing Classes of Regular Languages Using Prefix Codes of Bounded Synchronization Delay
Abstract
In this paper we continue a classical work of Schützenberger on codes with bounded synchronization delay. He was interested in characterizing those regular languages where the groups in the syntactic monoid belong to a variety H. He allowed operations on the language side which are union, intersection, concatenation and modified Kleene-star involving a mapping of a prefix code of bounded synchronization delay to a group G in H, but no complementation. In our notation this leads to the language classes SD_G(A^{infinity}) and SD_H(A^{infinity}). Our main result shows that SD_H(A^{infinity}) always corresponds to the languages having syntactic monoids where all subgroups are in H. Schützenberger showed this for a variety H if H contains Abelian groups, only. Our method shows the general result for all H directly on finite and infinite words. Furthermore, we introduce the notion of local Rees extensions which refers to a simple type of classical Rees extensions. We give a decomposition of a monoid in terms of its groups and local Rees extensions. This gives a somewhat similar, but simpler decomposition than in Rhodes' synthesis theorem. Moreover, we need a singly exponential number of operations, only. Finally, our decomposition yields an answer to a question in a recent paper of Almeida and Klíma about varieties that are closed under Rees extensions.
BibTeX - Entry
@InProceedings{diekert_et_al:LIPIcs:2016:6264,
author = {Volker Diekert and Tobias Walter},
title = {{Characterizing Classes of Regular Languages Using Prefix Codes of Bounded Synchronization Delay}},
booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
pages = {129:1--129:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-013-2},
ISSN = {1868-8969},
year = {2016},
volume = {55},
editor = {Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6264},
URN = {urn:nbn:de:0030-drops-62642},
doi = {10.4230/LIPIcs.ICALP.2016.129},
annote = {Keywords: formal language, synchronization delay, variety, Rees extension}
}
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Keywords: |
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formal language, synchronization delay, variety, Rees extension |
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Collection: |
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43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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23.08.2016 |
