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A Formalisation of Finite Automata Using Hereditarily Finite Sets

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Automated Deduction - CADE-25 (CADE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9195))

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Abstract

Hereditarily finite (HF) set theory provides a standard universe of sets, but with no infinite sets. Its utility is demonstrated through a formalisation of the theory of regular languages and finite automata, including the Myhill-Nerode theorem and Brzozowski’s minimisation algorithm. The states of an automaton are HF sets, possibly constructed by product, sum, powerset and similar operations.

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Notes

  1. 1.
    figure an

    denotes a typed universal set, here the set of all words.

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Acknowledgements

Christian Urban and Tobias Nipkow offered advice, and suggested Brzozowski’s minimisation algorithm as an example. The referees made a variety of useful comments.

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Authors and Affiliations

  1. Computer Laboratory, University of Cambridge, Cambridge, UK

    Lawrence C. Paulson

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  1. Lawrence C. Paulson
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Correspondence to Lawrence C. Paulson .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

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Paulson, L.C. (2015). A Formalisation of Finite Automata Using Hereditarily Finite Sets. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_15

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  • DOI: https://doi.org/10.1007/978-3-319-21401-6_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21400-9

  • Online ISBN: 978-3-319-21401-6

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