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DOI: 10.4230/LIPIcs.CSL.2017.13
URN: urn:nbn:de:0030-drops-77060
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7706/
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 | |
| Seminar: | 26th EACSL Annual Conference on Computer Science Logic (CSL 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 16.08.2017 |
