On selection functions that do not preserve normality

Wolfgang Merkle, Jan Reimann

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations

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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsBranislav Rovan, Peter Vojtas
PublisherSpringer Verlag
Pages602-611
Number of pages10
ISBN (Electronic)9783540406716
DOIs
StatePublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2747
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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