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.CSL.2017.13
URN: urn:nbn:de:0030-drops-77060
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7706/
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Borlido, Célia ; Czarnetzki, Silke ; Gehrke, Mai ; Krebs, Andreas

Stone Duality and the Substitution Principle

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Abstract

In this paper we relate two generalisations of the finite monoid recognisers of automata theory for the study of circuit complexity classes: Boolean spaces with internal monoids and typed monoids. Using the setting of stamps, this allows us to generalise a number of results from algebraic automata theory as it relates to Büchi's logic on words. We obtain an Eilenberg theorem, a substitution principle based on Stone duality, a block product principle for typed stamps and, as our main result, a topological semidirect product construction, which corresponds to the application of a general form of quantification. These results provide tools for the study of language classes given by logic fragments such as the Boolean circuit complexity classes.

BibTeX - Entry

@InProceedings{borlido_et_al:LIPIcs:2017:7706,
  author =	{C{\'e}lia Borlido and Silke Czarnetzki and Mai Gehrke and Andreas Krebs},
  title =	{{Stone Duality and the Substitution Principle}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Valentin Goranko and Mads Dam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7706},
  URN =		{urn:nbn:de:0030-drops-77060},
  doi =		{10.4230/LIPIcs.CSL.2017.13},
  annote =	{Keywords: C-variety of languages, typed monoid, Boolean space with an internal monoid, substitution principle, semidirect product}
}

Keywords: C-variety of languages, typed monoid, Boolean space with an internal monoid, substitution principle, semidirect product
Collection: 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)
Issue Date: 2017
Date of publication: 16.08.2017

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