Generalized Eilenberg Theorem I: Local Varieties of Languages

  • Jiří Adámek
  • Stefan Milius
  • Robert S. R. Myers
  • Henning Urbat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8412)


We investigate the duality between algebraic and coalgebraic recognition of languages to derive a generalization of the local version of Eilenberg’s theorem. This theorem states that the lattice of all boolean algebras of regular languages over an alphabet Σ closed under derivatives is isomorphic to the lattice of all pseudovarieties of Σ-generated monoids. By applying our method to different categories, we obtain three related results: one, due to Gehrke, Grigorieff and Pin, weakens boolean algebras to distributive lattices, one due to Polák weakens them to join-semilattices, and the last one considers vector spaces over ℤ2.


Boolean Algebra Full Subcategory Regular Language Subdirect Product Forgetful Functor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jiří Adámek
    • 1
  • Stefan Milius
    • 2
  • Robert S. R. Myers
    • 1
  • Henning Urbat
    • 1
  1. 1.Institut für Theoretische InformatikTechnische Universität BraunschweigGermany
  2. 2.Lehrstuhl für Theoretische InformatikFriedrich-Alexander-Universität Erlangen-NürnbergGermany

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