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Tree Automata as Algebras: Minimisation and Determinisation

Authors Gerco van Heerdt , Tobias Kappé , Jurriaan Rot, Matteo Sammartino , Alexandra Silva

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Author Details

Gerco van Heerdt
  • University College London, United Kingdom
Tobias Kappé
  • University College London, United Kingdom
Jurriaan Rot
  • University College London, United Kingdom
  • Radboud University, Nijmegen, The Netherlands
Matteo Sammartino
  • University College London, United Kingdom
Alexandra Silva
  • University College London, United Kingdom

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Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Matteo Sammartino, and Alexandra Silva. Tree Automata as Algebras: Minimisation and Determinisation. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We study a categorical generalisation of tree automata, as algebras for a fixed endofunctor endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm for these automata. We then build upon and extend an existing generalisation of the Nerode equivalence to a categorical setting and relate it to the existence of minimal automata. Finally, we show that generalised types of side-effects, such as non-determinism, can be captured by this categorical framework, leading to a general determinisation procedure.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • tree automata
  • algebras
  • minimisation
  • determinisation
  • Nerode equivalence


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