A Õ(n) Non-Adaptive Tester for Unateness

Khot and Shinkar (RANDOM, 2016) recently describe an adaptive, O(n log(n)/ε)-query tester for unateness of Boolean functions f : {0, 1}n 7→ {0, 1}. In this note, we describe a simple non-adaptive, O(n log(n/ε)/ε) -query tester for unateness for real-valued functions over the hypercube.

[1]  Rocco A. Servedio,et al.  Boolean Function Monotonicity Testing Requires (Almost) n 1/2 Non-adaptive Queries , 2014, STOC.

[2]  Eyal Kushilevitz,et al.  Distribution-Free Property Testing , 2003, RANDOM-APPROX.

[3]  Sofya Raskhodnikova,et al.  Lp-testing , 2014, STOC.

[4]  Rocco A. Servedio,et al.  New Algorithms and Lower Bounds for Monotonicity Testing , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[5]  Sourav Chakraborty,et al.  Monotonicity testing and shortest-path routing on the cube , 2010, Comb..

[6]  Seshadhri Comandur,et al.  Property Testing on Product Distributions , 2014, ACM Trans. Algorithms.

[7]  Subhash Khot,et al.  An Õ(n) Queries Adaptive Tester for Unateness , 2016, Electron. Colloquium Comput. Complex..

[8]  Eyal Kushilevitz,et al.  Testing Monotonicity over Graph Products , 2004, ICALP.

[9]  Dana Ron,et al.  Improved Testing Algorithms for Monotonicity , 1999, Electron. Colloquium Comput. Complex..

[10]  Eric Blais,et al.  A polynomial lower bound for testing monotonicity , 2016, STOC.

[11]  Kyomin Jung,et al.  Transitive-Closure Spanners , 2008, SIAM J. Comput..

[12]  Seshadhri Comandur,et al.  Optimal bounds for monotonicity and lipschitz testing over hypercubes and hypergrids , 2013, STOC '13.

[13]  Seshadhri Comandur,et al.  A o(n) monotonicity tester for boolean functions over the hypercube , 2013, STOC '13.

[14]  Ronitt Rubinfeld,et al.  Spot-checkers , 1998, STOC '98.

[15]  Dana Ron,et al.  Testing Monotonicity , 2000, Comb..

[16]  Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014 , 2014, STOC.