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arXiv · 1904.08802

Tree Automata as Algebras: Minimisation and Determinisation

Gerco van Heerdt·Tobias Kappé·Jurriaan Rot·Matteo Sammartino·Alexandra Silva
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Abstract

We study a categorical generalisation of tree automata, as $\Sigma$-algebras for a fixed endofunctor $\Sigma$ 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.

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Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Matteo Sammartino, Alexandra Silva. 2019-04-18. Tree Automata as Algebras: Minimisation and Determinisation. https://doi.org/10.4230/lipics.calco.2019.6

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