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DOI: 10.4230/LIPIcs.CALCO.2019.2
URN: urn:nbn:de:0030-drops-114309
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11430/
Milius, Stefan
From Equational Specifications of Algebras with Structure to Varieties of Data Languages (Invited Paper)
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Abstract
This extended abstract first presents a new category theoretic approach to equationally axiomatizable classes of algebras. This approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered algebras, continuous algebras, quantitative algebras, nominal algebras, or profinite algebras. We present a generic HSP theorem and a sound and complete equational logic, which encompass numerous flavors of equational axiomizations studied in the literature. In addition, we use the generic HSP theorem as a key ingredient to obtain Eilenberg-type correspondences yielding algebraic characterizations of properties of regular machine behaviours. When instantiated for orbit-finite nominal monoids, the generic HSP theorem yields a crucial step for the proof of the first Eilenberg-type variety theorem for data languages.
BibTeX - Entry
@InProceedings{milius:LIPIcs:2019:11430,
author = {Stefan Milius},
title = {{From Equational Specifications of Algebras with Structure to Varieties of Data Languages (Invited Paper)}},
booktitle = {8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
pages = {2:1--2:5},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-120-7},
ISSN = {1868-8969},
year = {2019},
volume = {139},
editor = {Markus Roggenbach and Ana Sokolova},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/11430},
URN = {urn:nbn:de:0030-drops-114309},
doi = {10.4230/LIPIcs.CALCO.2019.2},
annote = {Keywords: Birkhoff theorem, Equational logic, Eilenberg theorem, Data languages}
}
| Keywords: | Birkhoff theorem, Equational logic, Eilenberg theorem, Data languages | |
| Seminar: | 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 25.11.2019 |
