arXiv
Open Access
2019
The range of non-linear natural polynomials cannot be context-free
Dömötör Pálvölgyi
Abstrak
Suppose that some polynomial $f$ with rational coefficients takes only natural values at natural numbers, i.e., $L=\{f(n)\mid n\in \mathbb N\}\subset\mathbb N$. We show that the base-$q$ representation of $L$ is a context-free language if and only if $f$ is linear, answering a question of Shallit. The proof is based on a new criterion for context-freeness, which is a combination of the Interchange lemma and a generalization of the Pumping lemma.
Penulis (1)
D
Dömötör Pálvölgyi
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2019
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- en
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- arXiv
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- Open Access ✓