Abstract
We give an explicit function h : {0, 1}n → {0, 1} such that every deMorgan formula of size n3-o(1)/r2 agrees with h on at most a fraction of 1/2 + 2 -Ω(r)of the inputs. This improves the previous averagecase lower bound of Komargodski and Raz (STOC, 2013). Our technical contributions include a theorem that shows that the "expected shrinkage" result of Hastad (SIAM J. Comput., 1998) actually holds with very high probability (where the restrictions are chosen from a certain distribution that takes into account the structure of the formula), combining ideas of both Impagliazzo, Meka and Zuckerman (FOCS, 2012) and Komargodski and Raz. In addition, using a bit-fixing extractor in the construction of h allows us to simplify a major part of the analysis of Komargodski and Raz.
Original language | English (US) |
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Title of host publication | Proceedings - 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013 |
Pages | 588-597 |
Number of pages | 10 |
DOIs | |
State | Published - Dec 1 2013 |
Externally published | Yes |
Event | 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013 - Berkeley, CA, United States Duration: Oct 27 2013 → Oct 29 2013 |
Other
Other | 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, FOCS 2013 |
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Country/Territory | United States |
City | Berkeley, CA |
Period | 10/27/13 → 10/29/13 |
All Science Journal Classification (ASJC) codes
- Computer Science(all)