Abstract
The number of states in two-way deterministic finite automata (2DFAs) is considered. It is shown that the state complexity of basic operations is: at least m + n − o(m + n) and at most 4m + n + 1 for union; at least m + n − o(m + n) and at most m + n + 1 for intersection; at least n and at most 4n for complementation; at least \(\Omega(\frac{m}{n}) + \frac{2^{\Omega(n)}}{\log m}\) and at most \(2m^{m+1}\cdot 2^{n^{n+1}}\) for concatenation; at least \(\frac{1}{n} 2^{\frac{n}{2}-1}\) and at most \(2^{O(n^{n+1})}\) for both star and square; between n and n + 2 for reversal; exactly 2n for inverse homomorphism. In each case m and n denote the number of states in 2DFAs for the arguments.
Supported by VEGA grant 2/6089/26 and by Academy of Finland grant 118540.
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Jirásková, G., Okhotin, A. (2008). On the State Complexity of Operations on Two-Way Finite Automata. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_35
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DOI: https://doi.org/10.1007/978-3-540-85780-8_35
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