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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > ANAMAY TENGSE:
All reports by Author Anamay Tengse:

TR20-187 | 13th December 2020
Mrinal Kumar, C Ramya, Ramprasad Saptharishi, Anamay Tengse

If VNP is hard, then so are equations for it

Assuming that the Permanent polynomial requires algebraic circuits of exponential size, we show that the class VNP *does not* have efficiently computable equations. In other words, any nonzero polynomial that vanishes on the coefficient vectors of all polynomials in the class VNP requires algebraic circuits of super-polynomial size.

In a ... more >>>


TR20-063 | 29th April 2020
Prerona Chatterjee, Mrinal Kumar, C Ramya, Ramprasad Saptharishi, Anamay Tengse

On the Existence of Algebraically Natural Proofs

Revisions: 1

For every constant c > 0, we show that there is a family {P_{N,c}} of polynomials whose degree and algebraic circuit complexity are polynomially bounded in the number of variables, and that satisfies the following properties:
* For every family {f_n} of polynomials in VP, where f_n is an n ... more >>>


TR18-132 | 17th July 2018
Mrinal Kumar, Ramprasad Saptharishi, Anamay Tengse

Near-optimal Bootstrapping of Hitting Sets for Algebraic Circuits

Revisions: 2

The classical lemma of Ore-DeMillo-Lipton-Schwartz-Zippel states that any nonzero polynomial $f(x_1,\ldots, x_n)$ of degree at most $s$ will evaluate to a nonzero value at some point on a grid $S^n \subseteq \mathbb{F}^n$ with $|S| > s$. Thus, there is a deterministic polynomial identity test (PIT) for all degree-$s$ size-$s$ ... more >>>


TR17-135 | 10th September 2017
Ramprasad Saptharishi, Anamay Tengse

Quasi-polynomial Hitting Sets for Circuits with Restricted Parse Trees

Revisions: 1

We study the class of non-commutative Unambiguous circuits or Unique-Parse-Tree (UPT) circuits, and a related model of Few-Parse-Trees (FewPT) circuits (which were recently introduced by Lagarde, Malod and Perifel [LMP16] and Lagarde, Limaye and Srinivasan [LLS17]) and give the following constructions:
• An explicit hitting set of quasipolynomial size for ... more >>>




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