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Learning Deterministic Variable Automata over Infinite Alphabets

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Formal Methods – The Next 30 Years (FM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11800))

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Abstract

Automated reasoning about systems with infinite domains requires an extension of automata, and in particular, finite automata, to infinite alphabets. One such model is Variable Finite Automata (VFA). VFAs are finite automata whose alphabet is interpreted as variables that range over an infinite domain. On top of their simple and intuitive structure, VFAs have many appealing properties. One such property is a deterministic fragment (DVFA), which is closed under the Boolean operations, and whose containment and emptiness problems are decidable. These properties are rare amongst the many different models for automata over infinite alphabets. In this paper, we continue to explore the advantages of DVFAs, and show that they have a canonical form, which proves them to be a particularly robust model that is easy to reason about and use in practice. Building on these results, we construct an efficient learning algorithm for DVFAs, based on the \(\textsc {L}^*\) algorithm for regular languages.

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Notes

  1. 1.

    we omit the transitions labeled a from every state, for clarity of presentation.

  2. 2.

    It may be the case that \(\mathcal {L}\) can be expressed with even fewer than \(k'\) variables, by a non-ordered VFA. Here, we only consider ordered DVFA.

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Authors and Affiliations

  1. Department of Software Engineering, Braude College of Engineering, Karmiel, Israel

    Sarai Sheinvald

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  1. Sarai Sheinvald
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Correspondence to Sarai Sheinvald .

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Editors and Affiliations

  1. Consiglio Nazionale delle Ricerche, Pisa, Italy

    Maurice H. ter Beek

  2. Macquarie University, Sydney, NSW, Australia

    Annabelle McIver

  3. University of Minho, Braga, Portugal

    José N. Oliveira

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Sheinvald, S. (2019). Learning Deterministic Variable Automata over Infinite Alphabets. In: ter Beek, M., McIver, A., Oliveira, J. (eds) Formal Methods – The Next 30 Years. FM 2019. Lecture Notes in Computer Science(), vol 11800. Springer, Cham. https://doi.org/10.1007/978-3-030-30942-8_37

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  • DOI: https://doi.org/10.1007/978-3-030-30942-8_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-30941-1

  • Online ISBN: 978-3-030-30942-8

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