On Boolean decision trees with faulty nodes

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 probabilty. We show that f can be represented in k — DNF form and in j — CNF form, then O(n log(min{j, k/q})) queries suffice to compute f with probability of error less than q. This work uses a new approach to extend results of Feige, Raghavan, Peleg and Upfal, who proved the same bound for a narrower class of functions.

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