### Abstract

We consider the problem of identifying an unknown value x ε{lunate} {1, 2,..., n} using only comparisons of x to constants when as many as E of the comparisons may receive erroneous answers. For a continuous analogue of this problem we show that there is a unique strategy that is optimal in the worst case. This strategy for the continuous problem is then shown to yield a strategy for the original discrete problem that uses log_{2}n + E · log_{2}log_{2}n + O(E · log_{2}E) comparisons in the worst case. This number is shown to be optimal even if arbitrary "Yes-No" questions are allowed. We show that a modified version of this search problem with errors is equivalent to the problem of finding the minimal root of a set of increasing functions. The modified version is then also shown to be of complexity log_{2}n + E · log_{2}log_{2}n + O(E · log_{2}E).

Original language | English (US) |
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Pages (from-to) | 396-404 |

Number of pages | 9 |

Journal | Journal of Computer and System Sciences |

Volume | 20 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1980 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

*Journal of Computer and System Sciences*,

*20*(3), 396-404. https://doi.org/10.1016/0022-0000(80)90014-8