LIPIcs.STACS.2008.1321.pdf
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A Mahler's theorem for functions from words to integers
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25th International Symposium on Theoretical Aspects of Computer Science (STACS 2008)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2008-02-06
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Jean-Eric Pin and Pedro V. Silva. A Mahler's theorem for functions from words to integers. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 585-596, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/LIPIcs.STACS.2008.1321
https://doi.org/10.4230/LIPIcs.STACS.2008.1321
Abstract
In this paper, we prove an extension of Mahler's theorem, a
celebrated result of $p$-adic analysis. Mahler's original result
states that a function from $N$ to $Z$ is uniformly continuous for
the $p$-adic metric $d_p$ if and only if it can be uniformly
approximated by polynomial functions. We prove the same result for
functions from $A^*$ to $Z$, where $d_p$ is now the profinite
metric defined by $p$-groups (pro-$p$ metric).
Keywords
- $p$-adic topology
- binomial coefficients
- Mahler's theorem
- $p$-group languages
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