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Angluin Learning via Logic

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Logical Foundations of Computer Science (LFCS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10703))

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Abstract

In this paper we will provide a fresh take on Dana Angluin’s algorithm for learning using ideas from coalgebraic modal logic. Our work opens up possibilities for applications of tools & techniques from modal logic to automata learning and vice versa. As main technical result we obtain a generalisation of Angluin’s original algorithm from DFAs to coalgebras for an arbitrary finitary set functor T in the following sense: given a (possibly infinite) pointed T-coalgebra that we assume to be regular (i.e. having an equivalent finite representation) we can learn its finite representation by asking (i) “logical queries” (corresponding to membership queries) and (ii) making conjectures to which the teacher has to reply with a counterexample. This covers (a known variant) of the original L* algorithm and the learning of Mealy/Moore machines. Other examples are bisimulation quotients of (probabilistic) transition systems.

Supported by EPSRC grant EP/N015843/1.

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Notes

  1. 1.

    Readers should think of “behavioural equivalence” as a general notion of bisimilarity. In all concrete examples in this paper both notions of equivalence coincide.

  2. 2.

    Instead, we could use triples \((S,\varSigma ,\models _S)\) to be in line with [6] but we decided to leave the third “bookkeeping” component implicit.

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Acknowledgements

The authors would like to thank Nick Bezhanishvili and Alexandra Silva for helpful discussions and pointers to the literature.

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Authors and Affiliations

  1. Computer and Information Sciences, University of Strathclyde, Glasgow, Scotland

    Simone Barlocco & Clemens Kupke

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  1. Simone Barlocco
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  2. Clemens Kupke
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Correspondence to Clemens Kupke .

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Editors and Affiliations

  1. City University of New York, New York, New York, USA

    Sergei Artemov

  2. Cornell University, Ithaca, New York, USA

    Anil Nerode

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Barlocco, S., Kupke, C. (2018). Angluin Learning via Logic. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2018. Lecture Notes in Computer Science(), vol 10703. Springer, Cham. https://doi.org/10.1007/978-3-319-72056-2_5

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  • DOI: https://doi.org/10.1007/978-3-319-72056-2_5

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