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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > NONCOMMUTATIVE POLYNOMIALS:
Reports tagged with Noncommutative Polynomials:
TR22-022 | 18th February 2022
Vikraman Arvind, Pushkar Joglekar

On Efficient Noncommutative Polynomial Factorization via Higman Linearization

Revisions: 3

In this paper we study the problem of efficiently factorizing polynomials in the free noncommutative ring F of polynomials in noncommuting variables x_1,x_2,…,x_n over the field F. We obtain the following result:

Given a noncommutative arithmetic formula of size s computing a noncommutative polynomial f in F as input, where ... more >>>


TR22-042 | 31st March 2022
Vikraman Arvind, Pushkar Joglekar

Matrix Polynomial Factorization via Higman Linearization

In continuation to our recent work on noncommutative
polynomial factorization, we consider the factorization problem for
matrices of polynomials and show the following results.
\begin{itemize}
\item Given as input a full rank $d\times d$ matrix $M$ whose entries
$M_{ij}$ are polynomials in the free noncommutative ring
more >>>


TR24-198 | 10th November 2024
G V Sumukha Bharadwaj, Raja S

Randomized Black-Box PIT for Small Depth +-Regular Non-commutative Circuits

Revisions: 1

In this paper, we address the black-box polynomial identity testing (PIT) problem for non-commutative polynomials computed by $+$-regular circuits, a class of homogeneous circuits introduced by Arvind, Joglekar, Mukhopadhyay, and Raja (STOC 2017, Theory of Computing 2019). These circuits can compute polynomials with a number of monomials that are doubly ... more >>>




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