WNCG Seminar Series

Join CalTech's Dr. Quentin Berthet in this one-hour seminar. 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.