All reports by Author Prerona Chatterjee:

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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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TR23-001
| 5th January 2023
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Prerona Chatterjee, Pavel Hrubes#### New Lower Bounds against Homogeneous Non-Commutative Circuits

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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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TR21-037
| 1st March 2021
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Prerona Chatterjee#### Separating ABPs and Some Structured Formulas in the Non-Commutative Setting

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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: 1

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TR19-170
| 27th November 2019
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Prerona Chatterjee, Mrinal Kumar, Adrian She, Ben Lee Volk#### A Quadratic Lower Bound for Algebraic Branching Programs

Revisions: 3

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TR18-212
| 26th December 2018
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Prerona Chatterjee, Ramprasad Saptharishi#### Constructing Faithful Homomorphisms over Fields of Finite Characteristic

Revisions: 1

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, Pavel Hrubes

We give several new lower bounds on size of homogeneous non-commutative circuits. We present an explicit homogeneous bivariate polynomial of degree $d$ which requires homogeneous non-commutative circuit of size $\Omega(d/\log d)$. For an $n$-variate polynomial with $n>1$, the result can be improved to $\Omega(nd)$, if $d\leq n$, or $\Omega(nd \frac{\log ... 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 >>>

Prerona Chatterjee

The motivating question for this work is a long standing open problem, posed by Nisan (1991), regarding the relative powers of algebraic branching programs (ABPs) and formulas in the non-commutative setting. Even though the general question continues to remain open, we make some progress towards its resolution. To that effect, ... 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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Prerona Chatterjee, Mrinal Kumar, Adrian She, Ben Lee Volk

We show that any Algebraic Branching Program (ABP) computing the polynomial $\sum_{i = 1}^n x_i^n$ has at least $\Omega(n^2)$ vertices. This improves upon the lower bound of $\Omega(n\log n)$, which follows from the classical result of Baur and Strassen [Str73, BS83], and extends the results by Kumar [Kum19], which showed ... more >>>

Prerona Chatterjee, Ramprasad Saptharishi

We study the question of algebraic rank or transcendence degree preserving homomorphisms over finite fields. This concept was first introduced by Beecken, Mittmann and Saxena (Information and Computing, 2013), and exploited by them, and Agrawal, Saha, Saptharishi and Saxena (Journal of Computing, 2016) to design algebraic independence based identity tests ... more >>>