Research output per year
Research output per year
Irit Dinur, Or Meir
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
One of the major challenges of the research in circuit complexity is proving super-polynomial lower bounds for de-Morgan formulas. Karchmer, Raz, and Wigderson [20] suggested to approach this problem by proving that formula complexity behaves "as expected" with respect to the composition of functions f ⋄ g. They showed that this conjecture, if proved, would imply superpolynomial formula lower bounds. The first step toward proving the KRW conjecture was made by Edmonds et al. [10], who proved an analogue of the conjecture for the composition of "universal relations". In this work, we extend the argument of [10] further to f ⋄ g where f is an arbitrary function and g is the parity function. While this special case of the KRW conjecture was already proved implicitly in Håstad's work on random restrictions [14], our proof seems more likely to be generalizable to other cases of the conjecture. In particular, our proof uses an entirely different approach, based on communication complexity technique of Karchmer and Wigderson [21]. In addition, our proof gives a new structural result, which roughly says that the naive way for computing f ⋄ g is the only optimal way. Along the way, we obtain a new proof of the state-of-the-art formula lower bound of n3-o(1) due to [14].
Original language | English |
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Title of host publication | 31st Conference on Computational Complexity, CCC 2016 |
Editors | Ran Raz |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
Pages | 3:1-3:51 |
ISBN (Electronic) | 9783959770088 |
DOIs | |
State | Published - 1 May 2016 |
Event | 31st Conference on Computational Complexity, CCC 2016 - Tokyo, Japan Duration: 29 May 2016 → 1 Jun 2016 |
Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 50 |
ISSN (Print) | 1868-8969 |
Conference | 31st Conference on Computational Complexity, CCC 2016 |
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Country/Territory | Japan |
City | Tokyo |
Period | 29/05/16 → 1/06/16 |
Research output: Contribution to journal › Article › peer-review