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On Boolean Decision Trees with Faulty Nodes (1994)
| Venue: | In Random Structures and Algorithms |
| Citations: | 6 - 1 self |
BibTeX
@INPROCEEDINGS{Kenyon94onboolean,
author = {Claire Kenyon and Valerie King},
title = {On Boolean Decision Trees with Faulty Nodes},
booktitle = {In Random Structures and Algorithms},
year = {1994},
pages = {453--464}
}
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Abstract
We consider the problem of computing with faulty components in the context of the Boolean decision tree model, in which cost is measured by the number of input bits queried and the responses to queries are faulty with a fixed probability. We show that if f can be represented in k-DNF form and in j-CNF form, then O(n log(min(k; j)=q)) queries suffice to compute f with error probability less than q, where n is the number of input bits. 1 Introduction In this paper, we describe a method for performing reliable computation despite the presence of faulty components. This problem has been well studied in various contexts. The model we consider here is the noisy Boolean decision tree. In a Boolean decision tree, the value of a function on n bits is computed as follows: Each step consists of a query of an input bit, where the choice of the query may depend on the outcome of the previous queries. The cost Current address: LIP ENS-Lyon, 46 All'ee d'Italie, 69364 Lyon Cedex 07, France. Part...
