Note on Reversal of Binary Regular Languages
We present binary deterministic finite automata of n states that meet the upper bound 2n 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 2n. We also show that there is no regular language with state complexity 2n 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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