All reports by Author Anamay Tengse:

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TR24-119
| 14th July 2024
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Vishwas Bhargava, Anamay Tengse#### Explicit Commutative ROABPs from Partial Derivatives

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TR23-150
| 5th October 2023
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Prerona Chatterjee, Kshitij Gajjar, Anamay Tengse#### Monotone Classes Beyond VNP

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TR23-135
| 14th September 2023
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Prerona Chatterjee, Anamay Tengse#### On Annihilators of Explicit Polynomial Maps

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TR22-031
| 16th February 2022
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Prerona Chatterjee, Kshitij Gajjar, Anamay Tengse#### Transparency Beyond VNP in the Monotone Setting

Revisions: 5

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TR22-009
| 17th January 2022
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C. Ramya, Anamay Tengse#### On Finer Separations between Subclasses of Read-once Oblivious ABPs

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TR20-187
| 13th December 2020
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Mrinal Kumar, C Ramya, Ramprasad Saptharishi, Anamay Tengse#### If VNP is hard, then so are equations for it

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TR20-063
| 29th April 2020
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Prerona Chatterjee, Mrinal Kumar, C Ramya, Ramprasad Saptharishi, Anamay Tengse#### On the Existence of Algebraically Natural Proofs

Revisions: 2

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TR18-132
| 17th July 2018
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Mrinal Kumar, Ramprasad Saptharishi, Anamay Tengse#### Near-optimal Bootstrapping of Hitting Sets for Algebraic Circuits

Revisions: 3

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TR17-135
| 10th September 2017
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Ramprasad Saptharishi, Anamay Tengse#### Quasi-polynomial Hitting Sets for Circuits with Restricted Parse Trees

Revisions: 1

Vishwas Bhargava, Anamay Tengse

The dimension of partial derivatives (Nisan and Wigderson, 1997) is a popular measure for proving lower bounds in algebraic complexity. It is used to give strong lower bounds on the Waring decomposition of polynomials (called Waring rank). This naturally leads to an interesting open question: does this measure essentially characterize ... more >>>

Prerona Chatterjee, Kshitij Gajjar, Anamay Tengse

In this work, we study the natural monotone analogues of various equivalent definitions of VPSPACE: a well studied class (Poizat 2008, Koiran & Perifel 2009, Malod 2011, Mahajan & Rao 2013) that is believed to be larger than VNP. We observe that these monotone analogues are not equivalent unlike their ... more >>>

Prerona Chatterjee, Anamay Tengse

We study the algebraic complexity of annihilators of polynomials maps. In particular, when a polynomial map is `encoded by' a small algebraic circuit, we show that the coefficients of an annihilator of the map can be computed in PSPACE. Even when the underlying field is that of reals or complex ... more >>>

Prerona Chatterjee, Kshitij Gajjar, Anamay Tengse

Recently Hrubes and Yehudayoff (2021) showed a connection between the monotone algebraic circuit complexity of \emph{transparent} polynomials and a geometric complexity measure of their Newton polytope. They then used this connection to prove lower bounds against monotone VP (mVP). We extend their work by showing that their technique can be ... more >>>

C. Ramya, Anamay Tengse

Read-once Oblivious Algebraic Branching Programs (ROABPs) compute polynomials as products of univariate polynomials that have matrices as coefficients. In an attempt to understand the landscape of algebraic complexity classes surrounding ROABPs, we study classes of ROABPs based on the algebraic structure of these coefficient matrices. We study connections between polynomials ... more >>>

Mrinal Kumar, C Ramya, Ramprasad Saptharishi, Anamay Tengse

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 >>>

Prerona Chatterjee, Mrinal Kumar, C Ramya, Ramprasad Saptharishi, Anamay Tengse

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 ...
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Mrinal Kumar, Ramprasad Saptharishi, Anamay Tengse

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 >>>

Ramprasad Saptharishi, Anamay Tengse

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 ...
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