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oaioai:drops-oai.dagstuhl.de:5526

A Fibrational Approach to Automata Theory

Authors
Publication date
1 January 2015
Publisher
LIPIcs - Leibniz International Proceedings in Informatics. 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)
Doi

    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\u27s variety theorem along with several related results is obtained, covering uniformly varieties of languages and their coalgebraic modifications, Straubing\u27s C-varieties, and fully invariant local varieties

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