All reports by Author Nikhil Gupta:

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TR22-099
| 14th July 2022
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Nikhil Gupta, Chandan Saha, Bhargav Thankey#### Equivalence Test for Read-Once Arithmetic Formulas

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TR20-028
| 27th February 2020
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Nikhil Gupta, Chandan Saha, Bhargav Thankey#### A Super-Quadratic Lower Bound for Depth Four Arithmetic Circuits

Nikhil Gupta, Chandan Saha, Bhargav Thankey

We study the polynomial equivalence problem for orbits of read-once arithmetic formulas (ROFs). Read-once formulas have received considerable attention in both algebraic and Boolean complexity and have served as a testbed for developing effective tools and techniques for analyzing circuits. Two $n$-variate polynomials $f, g \in \mathbb{F}[\mathbf{x}]$ are equivalent, denoted ... more >>>

Nikhil Gupta, Chandan Saha, Bhargav Thankey

We show an $\widetilde{\Omega}(n^{2.5})$ lower bound for general depth four arithmetic circuits computing an explicit $n$-variate degree $\Theta(n)$ multilinear polynomial over any field of characteristic zero. To our knowledge, and as stated in the survey by Shpilka and Yehudayoff (FnT-TCS, 2010), no super-quadratic lower bound was known for depth four ... more >>>