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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2023.20
URN: urn:nbn:de:0030-drops-188174
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18817/
Boccali, Guido ;
Laretto, Andrea ;
Loregian, Fosco ;
Luneia, Stefano
Completeness for Categories of Generalized Automata ((Co)algebraic pearls)
Abstract
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 https://github.com/agda/agda-categories.
BibTeX - Entry
@InProceedings{boccali_et_al:LIPIcs.CALCO.2023.20,
author = {Boccali, Guido and Laretto, Andrea and Loregian, Fosco and Luneia, Stefano},
title = {{Completeness for Categories of Generalized Automata}},
booktitle = {10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
pages = {20:1--20:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-287-7},
ISSN = {1868-8969},
year = {2023},
volume = {270},
editor = {Baldan, Paolo and de Paiva, Valeria},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18817},
URN = {urn:nbn:de:0030-drops-188174},
doi = {10.4230/LIPIcs.CALCO.2023.20},
annote = {Keywords: Deterministic automata, Moore machines, Mealy machines, coalgebras, cocomplete category}
}
