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TCS+ Talk

Wednesday, October 13, 2021
10:00am to 11:00am
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Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits
Nutan Limaye, Associate Professor, Computer Science and Engineering, IT University of Copenhagen,

Abstract: Every multivariate polynomial P(X) can be written as a sum of monomials, i.e. a sum of products of variables and field constants. In general, the size of such an expression is the number of monomials that have a non-zero coefficient in P.

What happens if we add another layer of complexity, and consider sums of products of sums (of variables and field constants) expressions? Now, it becomes unclear how to prove that a given polynomial P(X) does not have small expressions. In this result, we solve exactly this problem.

More precisely, we prove that certain explicit polynomials have no polynomial-sized "Sigma-Pi-Sigma" (sums of products of sums) representations. We can also show similar results for Sigma-Pi-Sigma-Pi, Sigma-Pi-Sigma-Pi-Sigma and so on for all "constant-depth" expressions.  

The talk is based on a joint work of Nutan Limaye, Srikanth Srinivasan, and Sébastien Tavenas.

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  • Watching the live stream. At the announced start time of the talk (or a minute before), a live video stream will be available on our "next talk" page. Simply connect to the page and enjoy the talk. No webcam or registration is needed. Questions and comments during the talk are welcome (text only, unfortunately); simply post a comment below the live video stream on YouTube.
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For more information, please contact Bonnie Leung by email at bjleung@caltech.edu.