Complexity of Fault Tolerant Query Complexity

Abstract

In the model of fault tolerant decision trees introduced by Kenyon and Yao, there is a known upper bound E on the total number of queries that may be faulty (i.e., get the wrong bit). We consider this computational problem: Given as input the truth table of a function f : (0, 1)n → (0, 1) and a value of E, find the minimum possible height (worst-case number of queries) of any decision tree that computes f while tolerating up to E many faults. We design an algorithm for this problem that runs in time Oe(n+E/E) · (2E + 3)n), which is polynomial in the size of the truth table when E is a constant. This generalizes a standard algorithm for the non-fault tolerant setting.

Publication Title

Leibniz International Proceedings in Informatics, LIPIcs

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