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Electronic Colloquium on Computational Complexity

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All reports by Author Partha Mukhopadhyay:

TR20-166 | 9th November 2020
Arkadev Chattopadhyay, Rajit Datta, Partha Mukhopadhyay

Lower Bounds for Monotone Arithmetic Circuits Via Communication Complexity

Valiant (1980) showed that general arithmetic circuits with negation can be exponentially more powerful than monotone ones. We give the first qualitative improvement to this classical result: we construct a family of polynomials $P_n$ in $n$ variables, each of its monomials has positive coefficient, such that $P_n$ can be computed ... more >>>

TR19-063 | 28th April 2019
Vikraman Arvind, Abhranil Chatterjee, Rajit Datta, Partha Mukhopadhyay

Efficient Black-Box Identity Testing for Free Group Algebra

HrubeŇ° 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
more >>>

TR16-089 | 2nd June 2016
Vikraman Arvind, Partha Mukhopadhyay, Raja S

Randomized Polynomial Time Identity Testing for Noncommutative Circuits

Revisions: 2

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 >>>

TR15-052 | 6th April 2015
Partha Mukhopadhyay

Depth-4 Identity Testing and Noether's Normalization Lemma

Revisions: 1

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 ... more >>>

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