Abstract

This paper studies the depth of noisy decision trees in which each node gives the wrong answer with some constant probability. In the noisy Boolean decision tree model, tight bounds are given on the number of queries to input variables required to compute threshold functions, the parity function and symmetric functions. In the noisy comparison tree model, tight bounds are given on the number of noisy comparisons for searching, sorting, selection and merging. The paper also studies parallel selection and sorting with noisy comparisons, giving tight bounds for several problems.

MSC codes

  1. 68M15
  2. 68P10
  3. 68R05

Keywords

  1. fault-tolerance
  2. reliability
  3. noisy computation
  4. sorting and searching
  5. error-correction

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 1001 - 1018
ISSN (online): 1095-7111

History

Submitted: 4 March 1991
Accepted: 8 June 1993
Published online: 13 July 2006

MSC codes

  1. 68M15
  2. 68P10
  3. 68R05

Keywords

  1. fault-tolerance
  2. reliability
  3. noisy computation
  4. sorting and searching
  5. error-correction

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