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About this paper
Jiri Adamek, Stefan Milius, Robert Myers, Henning Urbat
Researchers at TU Braunschweig and FAU Erlangen-Nürnberg developed a generalized Eilenberg theorem within a categorical framework, demonstrating a bijective correspondence between varieties of languages in an abstract category C and pseudovarieties of monoids in a predual category D. This unification covers existing variants of Eilenberg's theorem and facilitates the discovery of new language-algebra correspondences, such as those linking languages closed under symmetric difference and intersection to monoids with 0.
Key insights
- Algebraic automata theory can be fundamentally understood as an interplay of duality and monoidal structures in a categorical setting.
- Language closure properties like derivatives and preimages can be fully characterized coalgebraically, which is essential for dualization to algebraic properties.
- The specific choice of predual categories C and D directly determines the nature of the Eilenberg-type correspondence that emerges.
Summary by alphaXiv.
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