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- W4381855770 abstract "We examine operational complexity assuming that the arguments are given as nondeterministic finite automata and the resulting language is represented by a deterministic finite automaton. We show that the known upper bounds for Boolean operations and concatenation are met by ternary languages, and we prove that they are asymptotically tight in the binary case. For the cut and square operations, we get tight upper bounds $$2^{m-1}(2^n+1)$$ and $$frac{3}{4}2^{2n}$$ , respectively. Our witnesses are described over a four-letter alphabet for cut, and a ten-letter alphabet for square. We also show that the tight upper bound on the syntactic complexity of a language given by an n-state NFA is $$2^{n^2}$$ . For the square root operation, we provide a lower bound $$2^{n^2-n}$$ and an upper bound $$2^{n^2}$$ ." @default.
- W4381855770 created "2023-06-25" @default.
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- W4381855770 date "2023-01-01" @default.
- W4381855770 modified "2023-09-27" @default.
- W4381855770 title "Operational Complexity: NFA-to-DFA Trade-Off" @default.
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- W4381855770 doi "https://doi.org/10.1007/978-3-031-34326-1_6" @default.
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