Completeness for Categories of Generalized Automata ((Co)algebraic pearls)

Authors Guido Boccali, Andrea Laretto, Fosco Loregian , Stefano Luneia

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Author Details

Guido Boccali
  • University of Torino, Italy
Andrea Laretto
  • Tallinn University of Technology, Estonia
Fosco Loregian
  • Tallinn University of Technology, Estonia
Stefano Luneia
  • University of Bologna, Italy


À René, parce qu'il faut ruser pour te lire.

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Guido Boccali, Andrea Laretto, Fosco Loregian, and Stefano Luneia. Completeness for Categories of Generalized Automata ((Co)algebraic pearls). In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We present a slick proof of completeness and cocompleteness for categories of F-automata, where the span of maps E ←d E⊗ I s→ O that usually defines a deterministic automaton of input I and output O in a monoidal category (K,⊗) is replaced by a span E ← FE → O for a generic endofunctor F : K → K of a generic category K: these automata exist in their "Mealy" and "Moore" version and form categories F-Mly and F-Mre; such categories can be presented as strict 2-pullbacks in Cat and whenever F is a left adjoint, both F-Mly and F-Mre admit all limits and colimits that K admits. We mechanize our main results using the proof assistant Agda and the library

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata extensions
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Formalisms
  • Deterministic automata
  • Moore machines
  • Mealy machines
  • coalgebras
  • cocomplete category


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