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To prove that P ≠ NP, it suffices to prove a superpolynomial lower bound on Boolean circuit complexity of a function from NP. Currently, we are not even close to achieving this goal: we do not know how to prove a 4n lower bound. What is more depressing is that there are almost no techniques for proving circuit lower bounds. In this note, we briefly review various approaches that could potentially lead to stronger linear or superlinear lower bounds for unrestricted Boolean circuits (i.e., circuits with no restriction on depth, fan-out, or basis).
Original language | English |
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Title of host publication | Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings |
Editors | Vladimir V. Podolskii, Fedor V. Fomin |
Publisher | Springer Nature |
Pages | 15-22 |
Number of pages | 8 |
ISBN (Print) | 9783319905297 |
DOIs | |
State | Published - 1 Jan 2018 |
Event | 13th International Computer Science Symposium in Russia, CSR 2018 - Moscow, Russian Federation Duration: 6 Jun 2018 → 10 Jun 2018 |
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10846 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference | 13th International Computer Science Symposium in Russia, CSR 2018 |
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Country/Territory | Russian Federation |
City | Moscow |
Period | 6/06/18 → 10/06/18 |
ID: 49820627