All reports by Author Rajit Datta:

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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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TR18-111
| 4th June 2018
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Vikraman Arvind, Abhranil Chatterjee, Rajit Datta, Partha Mukhopadhyay#### Beating Brute Force for Polynomial Identity Testing of General Depth-3 Circuits

Comments: 1

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TR17-074
| 29th April 2017
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Vikraman Arvind, Rajit Datta, Partha Mukhopadhyay, Raja S#### Efficient Identity Testing and Polynomial Factorization over Non-associative Free Rings

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, Abhranil Chatterjee, Rajit Datta, Partha Mukhopadhyay

Let $C$ be a depth-3 $\Sigma\Pi\Sigma$ arithmetic circuit of size $s$,

computing a polynomial $f \in \mathbb{F}[x_1,\ldots, x_n]$ (where $\mathbb{F}$ = $\mathbb{Q}$ or

$\mathbb{C}$) with fan-in of product gates bounded by $d$. We give a

deterministic time $2^d \text{poly}(n,s)$ polynomial identity testing

algorithm to check whether $f \equiv 0$ or ...
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Vikraman Arvind, Rajit Datta, Partha Mukhopadhyay, Raja S

In this paper we study arithmetic computations over non-associative, and non-commutative free polynomials ring $\mathbb{F}\{x_1,x_2,\ldots,x_n\}$. Prior to this work, the non-associative arithmetic model of computation was considered by Hrubes, Wigderson, and Yehudayoff [HWY10]. They were interested in completeness and explicit lower bound results.

We focus on two main problems ... more >>>