All reports by Author Partha Mukhopadhyay:

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TR19-063
| 28th April 2019
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Vikraman Arvind, Abhranil Chatterjee, Rajit Datta, Partha Mukhopadhyay#### Efficient Black-Box Identity Testing for Free Group Algebra

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TR16-089
| 2nd June 2016
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Vikraman Arvind, Partha Mukhopadhyay, Raja S#### Randomized Polynomial Time Identity Testing for Noncommutative Circuits

Revisions: 2

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TR15-052
| 6th April 2015
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Partha Mukhopadhyay#### Depth-4 Identity Testing and Noether's Normalization Lemma

Revisions: 1

Vikraman Arvind, Abhranil Chatterjee, Rajit Datta, Partha Mukhopadhyay

Hrubeš and Wigderson [HW14] initiated the study of

noncommutative arithmetic circuits with division computing a

noncommutative rational function in the free skew field, and

raised the question of rational identity testing. It is now known

that the problem can be solved in deterministic polynomial time in

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Vikraman Arvind, Partha Mukhopadhyay, Raja S

In this paper we show that polynomial identity testing for

noncommutative circuits of size $s$, computing a polynomial in

$\mathbb{F}\langle z_1,z_2,\cdots,z_n \rangle$, can be done by a randomized algorithm

with running time polynomial in $s$ and $n$. This answers a question

that has been open for over ten years.

The ... more >>>

Partha Mukhopadhyay

We consider the \emph{black-box} polynomial identity testing problem for a sub-class of

depth-4 circuits. Such circuits compute polynomials of the following type:

$

C(x) = \sum_{i=1}^k \prod_{j=1}^{d_i} Q_{i,j},

$

where $k$ is the fan-in of the top $\Sigma$ gate and $r$ is the maximum degree of the ...
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