The bounds on state-set size in the proofs of the equivalence between nondeterministic and deterministic finite automata and between two-way and one-way deterministic finite automata are considered. It is shown that the number of states in the subset machine in the first construction cannot be reduced for certain cases. It is also shown that the number of states in the one-way automation constructed in the second proof may be reduced only slightly.
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Frank R. Moore (1971) studied this question.
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