A Mahler's theorem for functions from words to integers

Pin, Jean-Eric; Silva, Pedro V.

doi:10.4230/LIPIcs.STACS.2008.1321

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A Mahler's theorem for functions from words to integers

Authors Jean-Eric Pin, Pedro V. Silva

Part of: Volume: 25th International Symposium on Theoretical Aspects of Computer Science (STACS 2008)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: 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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Document Identifiers

DOI: 10.4230/LIPIcs.STACS.2008.1321
URN: urn:nbn:de:0030-drops-13212

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Keywords

$p$-adic topology
binomial coefficients
Mahler's theorem
$p$-group languages

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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).

Cite As Get BibTex

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

Author Details

Jean-Eric Pin

Pedro V. Silva

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