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- W2954603477 abstract "We examine the deterministic and nondeterministic state complexity of square, power, positive closure, and complementation on star-free languages. For the state complexity of square, we get a non-trivial upper bound $$(n-1)2^n - 2(n-2)$$ and a lower bound of order $${Theta }(2^n)$$ . For the state complexity of the k-th power in the unary case, we get the tight upper bound $$k(n-1)+1$$ . Next, we show that the upper bound kn on the nondeterministic state complexity of the k-th power is met by a binary star-free language, while in the unary case, we have a lower bound $$k(n-1)+1$$ . For the positive closure, we show that the deterministic upper bound $$2^{n-1}+2^{n-2}-1$$ , as well as the nondeterministic upper bound n, can be met by star-free languages. We also show that in the unary case, the state complexity of positive closure is $$n^2-7n+13$$ , and the nondeterministic state complexity of complementation is between $$(n-1)^2+1$$ and $$n^2-2$$ ." @default.
- W2954603477 created "2019-07-12" @default.
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- W2954603477 date "2019-01-01" @default.
- W2954603477 modified "2023-09-26" @default.
- W2954603477 title "Square, Power, Positive Closure, and Complementation on Star-Free Languages" @default.
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- W2954603477 doi "https://doi.org/10.1007/978-3-030-23247-4_7" @default.
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