On Selection Functions that Do Not Preserve Normality

  title={On Selection Functions that Do Not Preserve Normality},
  author={Wolfgang Merkle and Jan Reimann},
The sequence selected from a sequence R(0)R(1) . . . by a language L is the subsequence of R that contains exactly the bits R(n + 1) such that the prefix R(0) . . . R(n) is in L. By a result of Agafonoff, a sequence is normal if and only if any subsequence selected by a regular language is again normal. Kamae and Weiss 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… CONTINUE READING

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