Theory Lunch Seminar

  • Ph.D. Student
  • Computer Science Department
  • Columbia University

A Polynomial Lower Bound for Monotonicity Testing of Boolean Functions

We prove a \tilde{\Omega}(n^{1/5}) lower bound on the query complexity of any non-adaptive two-sided error algorithm for testing whether an unknown n-variable Boolean function is monotone versus constant-far from monotone. This gives an exponential improvement on the previous lower bound of Omega(log n) due to Fischer et al from 2002. Our approach extends to give a similar lower bound for monotonicity testing of Boolean-valued functions over certain hypergrid domains {1,2,...,m}^n.

Joint work with Rocco Servedio.

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