All reports by Author Abhranil Chatterjee:

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TR23-075
| 17th May 2023
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Abhranil Chatterjee, Sumanta Ghosh, Rohit Gurjar, Roshan Raj#### Border Complexity of Symbolic Determinant under Rank One Restriction

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TR22-067
| 4th May 2022
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Vikraman Arvind, Abhranil Chatterjee, Partha Mukhopadhyay#### Black-box Identity Testing of Noncommutative Rational Formulas of Inversion Height Two in Deterministic Quasipolynomial-time

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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

Abhranil Chatterjee, Sumanta Ghosh, Rohit Gurjar, Roshan Raj

VBP is the class of polynomial families that can be computed by the determinant of a symbolic matrix of the form $A_0 + \sum_{i=1}^n A_ix_i$ where the size of each $A_i$ is polynomial in the number of variables (equivalently, computable by polynomial-sized algebraic branching programs (ABP)). A major open problem ... more >>>

Vikraman Arvind, Abhranil Chatterjee, Partha Mukhopadhyay

Hrube\v{s} and Wigderson (2015) initiated the complexity-theoretic study of noncommutative formulas with inverse gates. They introduced the Rational Identity Testing (RIT) problem which is to decide whether a noncommutative rational formula computes zero in the free skew field. In the white-box setting, deterministic polynomial-time algorithms are known for this problem ... more >>>

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

more >>>

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 ...
more >>>