Abstract
The reversal operation is well-studied in literature and the deterministic (respectively, nondeterministic) state complexity of reversal is known to be 2n (respectively, n). We consider the inversion operation where some substring of the given string is reversed. Formally, the inversion of a language L consists of all strings ux R v such that uxv ∈ L. We show that the nondeterministic state complexity of inversion is in Θ(n 3). We establish that the deterministic state complexity of the inversion is 2Ω(n ·logn), which is strictly worse than the worst case state complexity of the reversal operation. We also study the state complexity of different variants of the inversion operation, including prefix-, suffix-, and pseudo-inversion.
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Cho, DJ., Han, YS., Ko, SK., Salomaa, K. (2014). State Complexity of Inversion Operations. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_10
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DOI: https://doi.org/10.1007/978-3-319-09704-6_10
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