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A Formalisation of Finite Automata Using Hereditarily Finite Sets

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


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.


  • HF Sets
  • Hereditarily Finite (HF)
  • Myhill-Nerode Relation
  • Regular Languages
  • Minimal DFAs

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  1. 1.
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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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Correspondence to Lawrence C. Paulson .

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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.

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