From equational specifications of algebras with structure to varieties of data languages
Milius S (2019)
Publication Type: Conference contribution
Publication year: 2019
Journal
Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Book Volume: 139
Conference Proceedings Title: Leibniz International Proceedings in Informatics, LIPIcs
Event location: London
ISBN: 9783959771207
DOI: 10.4230/LIPIcs.CALCO.2019.2
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.
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How to cite
APA:
Milius, S. (2019). From equational specifications of algebras with structure to varieties of data languages. In Markus Roggenbach, Ana Sokolova (Eds.), Leibniz International Proceedings in Informatics, LIPIcs. London, GB: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.
MLA:
Milius, Stefan. "From equational specifications of algebras with structure to varieties of data languages." Proceedings of the 8th Conference on Algebra and Coalgebra in Computer Science, CALCO 2019, London Ed. Markus Roggenbach, Ana Sokolova, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2019.
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