Abstract
For each language L, let \(\hat{\mathcal F}_\cap(L)\) be the smallest intersection-closed full AFL generated by the language L. Furthermore, for each natural number k≥ 2 let \(P_k=\{a^{n^k}|n\in\mathbb N\}\). By applying certain classical and recent results on Diophantine equations we show that \(\mathcal L_{RE}=\hat{\mathcal F}_\cap(P_k)\), i.e., the family of all recursively enumerable languages coincides with the smallest intersection-closed full AFL generated by the polynomial language P k for all k≥ 2. This allows us to answer to an open problem of S. Ginsburg and J. Goldstine in [2].
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© 2005 Springer-Verlag Berlin Heidelberg
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Kortelainen, J. (2005). Polynomial Generators of Recursively Enumerable Languages. In: De Felice, C., Restivo, A. (eds) Developments in Language Theory. DLT 2005. Lecture Notes in Computer Science, vol 3572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505877_28
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DOI: https://doi.org/10.1007/11505877_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26546-7
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