PhD Seminar • Algorithms and Complexity — Lower Bounds for Tolerant Junta and Unateness Testing via Rejection Sampling of GraphsExport this event to calendar

Wednesday, March 13, 2019 — 1:30 PM EDT

Amit Levi, PhD candidate
David R. Cheriton School of Computer Science

We introduce a new model for testing graph properties which we call the {rejection sampling model}. We show that testing bipartiteness of n-nodes graphs using rejection sampling queries requires complexity Ω(n^2). Via reductions from the rejection sampling model, we give three new lower bounds for tolerant testing of Boolean functions of the form f:{0,1}^n→{0,1}:

  • Tolerant k-junta testing with {non-adaptive} queries requires Ω(k^2) queries.
  • Tolerant unateness testing requires Ω(n) queries.
  • Tolerant unateness testing with {non-adaptive} queries requires Ω(n^3/2) queries.

Given the O(k^3/2)-query non-adaptive junta tester of Blais, we conclude that non-adaptive tolerant junta testing requires more queries than non-tolerant junta testing. In addition, given the O(n^3/4)-query unateness tester of Chen, Waingarten, and Xie and the O(n)-query non-adaptive unateness tester of Baleshzar, Chakrabarty, Pallavoor, Raskhodnikova, and Seshadhri, we conclude that tolerant unateness testing requires more queries than non-tolerant unateness testing, in both adaptive and non-adaptive settings. These lower bounds provide the first separation between tolerant and non-tolerant testing for a natural property of Boolean functions.

Location 
MC - Mathematics & Computer Building
5501
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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