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On Selection Functions that Do Not Preserve Normality

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Mathematical Foundations of Computer Science 2003 (MFCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2747))

Abstract

The sequence selected from a sequence R(0)R(1)... by a language L is the subsequence of all bits R(n+1) such that the prefix R(0)... R(n) is in L. By a result of Agafonoff [1], a sequence is normal if and only if any subsequence selected by a regular language is again normal. Kamae and Weiss [11] and others have raised the question of how complex a language must be such that selecting according to the language does not preserve normality. We show that there are such languages that are only slightly more complicated than regular ones, namely, normality is neither preserved by linear languages nor by deterministic one-counter languages. In fact, for both types of languages it is possible to select a constant sequence from a normal one.

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Authors and Affiliations

  1. Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 294, D-69120, Heidelberg, Germany

    Wolfgang Merkle & Jan Reimann

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  1. Wolfgang Merkle
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  2. Jan Reimann
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Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia

    Branislav Rovan

  2. Charles University, Prague, Czech Republic

    Peter Vojtáš

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Merkle, W., Reimann, J. (2003). On Selection Functions that Do Not Preserve Normality. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_54

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  • DOI: https://doi.org/10.1007/978-3-540-45138-9_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40671-6

  • Online ISBN: 978-3-540-45138-9

  • eBook Packages: Springer Book Archive

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