Abstract
The GF(2)-inverse operation on formal languages is known to have state complexity \(2^n+1\) for alphabets with at least three symbols, and \(2^{n-1}+1\) for a one-symbol alphabet. In this paper, it is shown that, for a two-symbol alphabet, its state complexity is exactly \(\frac{3}{4}2^n + 3\). For a more general operation of GF(2)-star, its state complexity for a binary alphabet remains \(2^n+1\).
Supported by Russian Science Foundation, project 18-11-00100.
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Okhotin, A., Sazhneva, E. (2020). State Complexity of GF(2)-inverse and GF(2)-star on Binary Languages. In: Jirásková, G., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2020. Lecture Notes in Computer Science(), vol 12442. Springer, Cham. https://doi.org/10.1007/978-3-030-62536-8_12
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