eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-12-14
26:1
26:11
10.4230/LIPIcs.FSTTCS.2022.26
article
Complexity of Fault Tolerant Query Complexity
Maharjan, Ramita
1
Watson, Thomas
1
University of Memphis, TN, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol250-fsttcs2022/LIPIcs.FSTTCS.2022.26/LIPIcs.FSTTCS.2022.26.pdf
Fault
Tolerant
Query
Complexity