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Electronic Colloquium on Computational Complexity

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All reports by Author Ankit Garg:

TR21-155 | 13th November 2021
Vishwas Bhargava, Ankit Garg, Neeraj Kayal, Chandan Saha

Learning generalized depth-three arithmetic circuits in the non-degenerate case

Revisions: 1

Consider a homogeneous degree $d$ polynomial $f = T_1 + \cdots + T_s$, $T_i = g_i(\ell_{i,1}, \ldots, \ell_{i, m})$ where $g_i$'s are homogeneous $m$-variate degree $d$ polynomials and $\ell_{i,j}$'s are linear polynomials in $n$ variables. We design a (randomized) learning algorithm that given black-box access to $f$, computes black-boxes for ... more >>>

TR20-132 | 7th September 2020
Arkadev Chattopadhyay, Ankit Garg, Suhail Sherif

Towards Stronger Counterexamples to the Log-Approximate-Rank Conjecture

We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at most $O(n^3)$ and randomized parity decision tree complexity $\Theta(n)$. This improves upon the ... more >>>

TR19-140 | 7th October 2019
Ankit Garg, Visu Makam, Rafael Mendes de Oliveira, Avi Wigderson

Search problems in algebraic complexity, GCT, and hardness of generator for invariant rings.

Revisions: 1

We consider the problem of outputting succinct encodings of lists of generators for invariant rings. Mulmuley conjectured that there are always polynomial sized such encodings for all invariant rings. We provide simple examples that disprove this conjecture (under standard complexity assumptions).

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