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Dmitry Sokolov: (Semi)Algebraic Proofs over $\{\pm 1\}$ Variables Sokolov, Dmitry
Description
One of the major open problem in proof complexity is to prove lower bounds on $AC_0[p]$-Frege proof systems. As a step toward this goal Impagliazzo, Mouli and Pitassi in a recent paper suggested to prove lower bounds on the size for Polynomial Calculus over the $\{\pm 1\}$ basis. In this talk we show a technique for proving such lower bounds and moreover we also give lower bounds on the size for Sum-of-Squares over the $\{\pm 1\}$ basis. We show lower bounds on random $\Delta$-CNF formulas and formulas composed with a gadget. As a byproduct, we establish a separation between Polynomial Calculus and Sum-of-Squares over the $\{\pm 1\}$ basis by proving a lower bound on the Pigeonhole Principle.
Item Metadata
Title |
Dmitry Sokolov: (Semi)Algebraic Proofs over $\{\pm 1\}$ Variables
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2020-01-20T16:57
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Description |
One of the major open problem in proof complexity is to prove lower bounds on $AC_0[p]$-Frege proof
systems. As a step toward this goal Impagliazzo, Mouli and Pitassi in a recent paper suggested to prove
lower bounds on the size for Polynomial Calculus over the $\{\pm 1\}$ basis. In this talk we show a
technique for proving such lower bounds and moreover we also give lower bounds on the size for
Sum-of-Squares over the $\{\pm 1\}$ basis.
We show lower bounds on random $\Delta$-CNF formulas and formulas composed with a gadget. As a byproduct,
we establish a separation between Polynomial Calculus and Sum-of-Squares over the $\{\pm 1\}$ basis by
proving a lower bound on the Pigeonhole Principle.
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Extent |
35.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Lund University
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Series | |
Date Available |
2020-07-19
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0392455
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International