License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2022.26
URN: urn:nbn:de:0030-drops-174185
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17418/
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Maharjan, Ramita ; Watson, Thomas

Complexity of Fault Tolerant Query Complexity

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LIPIcs-FSTTCS-2022-26.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{maharjan_et_al:LIPIcs.FSTTCS.2022.26,
  author =	{Maharjan, Ramita and Watson, Thomas},
  title =	{{Complexity of Fault Tolerant Query Complexity}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{26:1--26:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17418},
  URN =		{urn:nbn:de:0030-drops-174185},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.26},
  annote =	{Keywords: Fault, Tolerant, Query, Complexity}
}

Keywords: Fault, Tolerant, Query, Complexity
Collection: 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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