Note on Reversal of Binary Regular Languages
We present binary deterministic finite automata of n states that meet the upper bound 2 n on the state complexity of reversal. The automata have a single final state and are one-cycle-free-path, thus the witness languages are deterministic union-free. This result allows us to describe a binary language such that the nondeterministic state complexity of the language and of its complement is n and n + 1, respectively, while the state complexity of the language is 2 n . We also show that there is no regular language with state complexity 2 n such that both the language and its complement have nondeterministic state complexity n.
KeywordsRegular languages reversal state complexity nondeterministic state complexity deterministic union-free languages
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