A Fibrational Approach to Automata Theory

Chen, Liang-Ting; Urbat, Henning

doi:10.4230/LIPIcs.CALCO.2015.50

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A Fibrational Approach to Automata Theory

Authors Liang-Ting Chen, Henning Urbat

Part of: Volume: 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Conference on Algebra and Coalgebra in Computer Science (CALCO)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2015-10-28

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Document Identifiers

DOI: 10.4230/LIPIcs.CALCO.2015.50
URN: urn:nbn:de:0030-drops-55268

Subject Classification

Keywords

Eilenberg’s variety theorem
duality
coalgebra
Grothendieck fibration

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Abstract

For predual categories C and D we establish isomorphisms between opfibrations representing local varieties of languages in C, local pseudovarieties of D-monoids, and finitely generated profinite D-monoids. The global sections of these opfibrations are shown to correspond to varieties of languages in C, pseudovarieties of D-monoids, and profinite equational theories of D-monoids, respectively. As an application, a new proof of Eilenberg's variety theorem along with several related results is obtained, covering uniformly varieties of languages and their coalgebraic modifications, Straubing's C-varieties, and fully invariant local varieties.

Cite As Get BibTex

Liang-Ting Chen and Henning Urbat. A Fibrational Approach to Automata Theory. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 50-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.CALCO.2015.50

Author Details

Liang-Ting Chen

Henning Urbat

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