Nondeterministic Direct Product Reductions and the Success Probability of SAT Solvers
, Institute for Advanced Study
Date: Tuesday, December 10, 2013
Time: 4:15 PM to 5:15 PM Note: all times are in the Eastern Time Zone
Refreshments: 3:45 PM
Host: Scott Aaronson
Contact: Holly A Jones, firstname.lastname@example.org
Relevant URL: http://toc.csail.mit.edu/node/375
Speaker URL: None
email@example.com, firstname.lastname@example.org, email@example.com
TALK: Nondeterministic Direct Product Reductions and the Success Probability of SAT Solvers
Abstract: In this talk I will describe nondeterministic reductions which yield new direct product theorems (DPTs) for Boolean circuits. In our theorems one assumes that a function F is "mildly hard" against *nondeterministic* circuits of some size s(n), and concludes that the t-fold direct product F^t is "extremely hard" against probabilistic circuits of only polynomially smaller size s'(n). The main advantage of these results compared with previous DPTs is the strength of the size bound in our conclusion. As an application, we show that if NP is not in coNP/poly then, for every PPT algorithm attempting to produce satisfying assignments to Boolean formulas, there are infinitely many satisfiable instances on which the algorithm's success probability is nearly-exponentially small. This furthers a project of Paturi and Pudlák [STOC'10].
Created by Holly A Jones at Tuesday, November 19, 2013 at 3:22 PM.