Zobrazeno 1 - 10
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pro vyhledávání: '"Joglekar, Pushkar"'
Autor:
Arvind, Vikraman, Joglekar, Pushkar S
We study the noncommutative rank problem, ncRANK, of computing the rank of matrices with linear entries in $n$ noncommuting variables and the problem of noncommutative Rational Identity Testing, RIT, which is to decide if a given rational formula in
Externí odkaz:
http://arxiv.org/abs/2404.16382
Autor:
Arvind, V., Joglekar, Pushkar S.
Based on a theorem of Bergman we show that multivariate noncommutative polynomial factorization is deterministic polynomial-time reducible to the factorization of bivariate noncommutative polynomials. More precisely, we show the following: (1) In the
Externí odkaz:
http://arxiv.org/abs/2303.06001
Autor:
Arvind, V., Joglekar, Pushkar S.
In continuation to our recent work on noncommutative polynomial factorization, we consider the factorization problem for matrices of polynomials and show the following results. (1) Given as input a full rank $d\times d$ matrix $M$ whose entries $M_{i
Externí odkaz:
http://arxiv.org/abs/2203.16978
Autor:
Arvind, V., Joglekar, Pushkar S.
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 noncommut
Externí odkaz:
http://arxiv.org/abs/2202.09883
Autor:
Arvind, V., Joglekar, Pushkar S.
Publikováno v:
In Information and Computation December 2024 301 Part A
One of the major problems writers and poets face is the writer's block. It is a condition in which an author loses the ability to produce new work or experiences a creative slowdown. The problem is more difficult in the context of poetry than prose,
Externí odkaz:
http://arxiv.org/abs/2107.14587
An efficient randomized polynomial identity test for noncommutative polynomials given by noncommutative arithmetic circuits remains an open problem. The main bottleneck to applying known techniques is that a noncommutative circuit of size $s$ can com
Externí odkaz:
http://arxiv.org/abs/1611.07235
Autor:
Aravind, N. R., Joglekar, Pushkar S.
We introduce and study the notion of read-$k$ projections of the determinant: a polynomial $f \in \mathbb{F}[x_1, \ldots, x_n]$ is called a {\it read-$k$ projection of determinant} if $f=det(M)$, where entries of matrix $M$ are either field elements
Externí odkaz:
http://arxiv.org/abs/1508.06511
In this paper we explore the noncommutative analogues, $\mathrm{VP}_{nc}$ and $\mathrm{VNP}_{nc}$, of Valiant's algebraic complexity classes and show some striking connections to classical formal language theory. Our main results are the following: (
Externí odkaz:
http://arxiv.org/abs/1508.00395
In this paper we study the complexity of factorization of polynomials in the free noncommutative ring $\mathbb{F}\langle x_1,x_2,\dots,x_n\rangle$ of polynomials over the field $\mathbb{F}$ and noncommuting variables $x_1,x_2,\ldots,x_n$. Our main re
Externí odkaz:
http://arxiv.org/abs/1501.00671