Friday, April 17, 2015
12:00 pm

Theory of Computing Seminar

Detection of Planted Solutions for Flat Satisfiability Problems
Quentin Berthet, Caltech


We study the detection problem of finding planted solutions in random instances of flat satisfiability problems, a generalization of boolean satisfiability formulas. We describe the properties of random instances
of flat satisfiability, as well of the optimal rates of detection of the  associated hypothesis testing problem. We also study the performance of an algorithmically efficient testing procedure. Introducing a modification of our model, the light planting of solutions, allows us to hint strongly at the difficulty of detecting planted flat satisfiability for a wide class of tests, by relating this problem to learning parity with noise. 
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