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A Categorical Framework for Learning Generalised Tree Automata

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Coalgebraic Methods in Computer Science (CMCS 2022)

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Abstract

Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify these using category theory in order to ease correctness proofs and guide the design of new algorithms. In this paper, we extend CALF to cover learning of algebraic structures that may not have a coalgebraic presentation. Furthermore, we provide a detailed algorithmic account of an abstract version of the popular \(\mathtt {L}^{\!\star }\) algorithm, which was missing from CALF. We instantiate the abstract theory to a large class of \(\mathbf {Set}\) functors, by which we recover for the first time practical tree automata learning algorithms from an abstract framework and at the same time obtain new algorithms to learn algebras of quotiented polynomial functors.

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Notes

  1. 1.

    http://www.calf-project.org.

  2. 2.

    Recursive coalgebras have been used to generalise prefix-closedness in an automata learning context in earlier work [24], as well as to generalise counterexamples [12, 41].

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Acknowledgements

T. Kappé was partially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101027412 (VERLAN), as well as ERC Starting Grant 679127 (ProFoundNet). Gerco van Heerdt, Matteo Sammartino, and Alexandra Silva were partially supported by the EPSRC Standard Grant CLeVer (EP/S028641/1).

Author information

Authors and Affiliations

  1. University College London, London, UK

    Gerco van Heerdt, Matteo Sammartino & Alexandra Silva

  2. ILLC, University of Amsterdam, Amsterdam, The Netherlands

    Tobias Kappé

  3. Radboud University, Nijmegen, The Netherlands

    Jurriaan Rot

  4. Royal Holloway, University of London, Egham, UK

    Matteo Sammartino

  5. Cornell University, Ithaca, USA

    Alexandra Silva

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  1. Gerco van Heerdt
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  5. Alexandra Silva
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Correspondence to Gerco van Heerdt .

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Editors and Affiliations

  1. University of Groningen, Groningen, The Netherlands

    Helle Hvid Hansen

  2. University College London, London, UK

    Fabio Zanasi

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Heerdt, G.v., Kappé, T., Rot, J., Sammartino, M., Silva, A. (2022). A Categorical Framework for Learning Generalised Tree Automata. In: Hansen, H.H., Zanasi, F. (eds) Coalgebraic Methods in Computer Science. CMCS 2022. Lecture Notes in Computer Science, vol 13225. Springer, Cham. https://doi.org/10.1007/978-3-031-10736-8_4

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