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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > ABHRANIL CHATTERJEE:
All reports by Author Abhranil Chatterjee:

TR24-150 | 2nd October 2024
Abhranil Chatterjee, Sumanta Ghosh, Rohit Gurjar, Roshan Raj

Characterizing and Testing Principal Minor Equivalence of Matrices

Two matrices are said to be principal minor equivalent if they have equal
corresponding principal minors of all orders. We give a characterization of
principal minor equivalence and a deterministic polynomial time algorithm to
check if two given matrices are principal minor equivalent. Earlier such
results were known for ... more >>>


TR24-073 | 11th April 2024
Vikraman Arvind, Abhranil Chatterjee, Partha Mukhopadhyay

Trading Determinism for Noncommutativity in Edmonds' Problem

Let $X=X_1\sqcup X_2\sqcup\ldots\sqcup X_k$ be a partitioned set of variables such that the variables in each part $X_i$ are noncommuting but for any $i\neq j$, the variables $x \in X_i$ commute with the variables $x' \in X_j$. Given as input a square matrix $T$ whose entries are linear forms over ... more >>>


TR23-147 | 27th September 2023
Vikraman Arvind, Abhranil Chatterjee, Partha Mukhopadhyay

Black-Box Identity Testing of Noncommutative Rational Formulas in Deterministic Quasipolynomial Time

Revisions: 5 , Comments: 1

Rational Identity Testing (RIT) is the decision problem of determining whether or not a given noncommutative rational formula computes zero in the free skew field. It admits a deterministic polynomial-time white-box algorithm [Garg et al., 2016; Ivanyos et al., 2018; Hamada and Hirai, 2021], and a randomized polynomial-time black-box algorithm ... more >>>


TR23-122 | 9th August 2023
Vikraman Arvind, Abhranil Chatterjee

On Lifting Lower Bounds for Noncommutative Circuits using Automata

We revisit the main result of Carmosino et al \cite{CILM18} which shows that an $\Omega(n^{\omega/2+\epsilon})$ size noncommutative arithmetic circuit size lower bound (where $\omega$ is the matrix multiplication exponent) for a constant-degree $n$-variate polynomial family $(g_n)_n$, where each $g_n$ is a noncommutative polynomial, can be ``lifted'' to an exponential size ... more >>>


TR23-115 | 8th August 2023
Abhranil Chatterjee, Mrinal Kumar, Ben Lee Volk

Determinants vs. Algebraic Branching Programs

Revisions: 1

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 >>>


TR23-075 | 17th May 2023
Abhranil Chatterjee, Sumanta Ghosh, Rohit Gurjar, Roshan Raj

Border Complexity of Symbolic Determinant under Rank One Restriction

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 >>>


TR22-067 | 4th May 2022
Vikraman Arvind, Abhranil Chatterjee, Partha Mukhopadhyay

Black-box Identity Testing of Noncommutative Rational Formulas of Inversion Height Two in Deterministic Quasipolynomial-time

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 >>>


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

Efficient Black-Box Identity Testing for Free Group Algebra

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 >>>


TR18-111 | 4th June 2018
Vikraman Arvind, Abhranil Chatterjee, Rajit Datta, Partha Mukhopadhyay

Beating Brute Force for Polynomial Identity Testing of General Depth-3 Circuits

Comments: 1

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 >>>




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