All reports by Author Mrinal Kumar:

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TR23-115
| 8th August 2023
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Abhranil Chatterjee, Mrinal Kumar, Ben Lee Volk#### Determinants vs. Algebraic Branching Programs

Revisions: 1

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TR21-163
| 19th November 2021
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Siddharth Bhandari, Prahladh Harsha, Mrinal Kumar, A. Shankar#### Algorithmizing the Multiplicity Schwartz-Zippel Lemma

Revisions: 1

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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: 1

Abhranil Chatterjee, Mrinal Kumar, Ben Lee Volk

We show that for every homogeneous polynomial of degree $d$, if it has determinantal complexity at most $s$, then it can be computed by a homogeneous algebraic branching program (ABP) of size at most $O(d^5s)$. Moreover, we show that for \textit{most} homogeneous polynomials, the width of the resulting homogeneous ABP ... more >>>

Siddharth Bhandari, Prahladh Harsha, Mrinal Kumar, A. Shankar

The multiplicity Schwartz-Zippel lemma asserts that over a field, a low-degree polynomial cannot vanish with high multiplicity very often on a sufficiently large product set. Since its discovery in a work of Dvir, Kopparty, Saraf and Sudan [DKSS13], the lemma has found nu- merous applications in both math and computer ... 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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