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A Formalisation of Finite Automata using Hereditarily Finite Sets (1505.01662v1)
Published 7 May 2015 in cs.FL and cs.LO
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.