### Abstract

We consider the problem of identifying an unknown value xe{l, 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-Iog_{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+0(E-log_{2}E).

Original language | English (US) |
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Pages (from-to) | 227-232 |

Number of pages | 6 |

Journal | Proceedings of the Annual ACM Symposium on Theory of Computing |

DOIs | |

State | Published - May 1 1978 |

Event | 10th Annual ACM Symposium on Theory of Computing, STOC 1978 - San Diego, United States Duration: May 1 1978 → May 3 1978 |

### ASJC Scopus subject areas

- Software

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## Cite this

*Proceedings of the Annual ACM Symposium on Theory of Computing*, 227-232. https://doi.org/10.1145/800133.804351