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Complexity of Fault Tolerant Query Complexity

Authors Ramita Maharjan, Thomas Watson

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Author Details

Ramita Maharjan
  • University of Memphis, TN, USA
Thomas Watson
  • University of Memphis, TN, USA

Funding

This work was supported by NSF grant CCF-1657377.

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Ramita Maharjan and Thomas Watson. Complexity of Fault Tolerant Query Complexity. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 26:1-26:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.FSTTCS.2022.26

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 Õ(binom(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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Fault
  • Tolerant
  • Query
  • Complexity

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