Abstract
We prove that for any rational number \(\alpha >1\) there exists a semi-Thue system with derivational complexity function belonging to the asymptotic class \(\varTheta (n^{\alpha })\). In particular, we answer a question of Y. Kobayashi, whether there exists a semi-Thue system whose derivational complexity function is in the class \(\varTheta (n^{\alpha })\) with \(\alpha \in (1,2)\).
This work was supported by a research grant from Russian Science Foundation, project no. 16-11-10252.
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Notes
- 1.
After the preliminary version of this paper became partly available to the public, several examples of systems, which do not preserve length, have been constructed. An anonymous referee suggested a construction of a system having complexity \(\varTheta (n \log ^* n)\) and recently Y. Kobayashi announced an example of a system with derivational complexity function from the class \(\varTheta (n \log \log n\)).
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Acknowledgements
The author would like to thank Jean-Camille Birget (Rutgers University at Camden) and Daria Smirnova (Université de Genève) for stimulating discussions. The author is also indebted to several anonymous referees whose comments significantly improved the quality of this paper.
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Talambutsa, A. (2020). On Subquadratic Derivational Complexity of Semi-Thue Systems. In: Fernau, H. (eds) Computer Science – Theory and Applications. CSR 2020. Lecture Notes in Computer Science(), vol 12159. Springer, Cham. https://doi.org/10.1007/978-3-030-50026-9_28
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DOI: https://doi.org/10.1007/978-3-030-50026-9_28
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