Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Diekert, Volker; Walter, Tobias http://www.dagstuhl.de/lipics License
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Characterizing Classes of Regular Languages Using Prefix Codes of Bounded Synchronization Delay

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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}
}

Keywords: formal language, synchronization delay, variety, Rees extension
Seminar: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue date: 2016
Date of publication: 2016


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