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pro vyhledávání: '"Joglekar, Pushkar S"'
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 $M_{i
Externí odkaz:
http://arxiv.org/abs/2203.16978
Autor:
Arvind, V., Joglekar, Pushkar S.
In this paper we study the problem of efficiently factorizing polynomials in the free noncommutative ring F of polynomials in noncommuting variables x_1,x_2,..., x_n over the field F. We obtain the following result: Given a noncommut
Externí odkaz:
http://arxiv.org/abs/2202.09883
Autor:
Arvind, V., Joglekar, Pushkar S.
Publikováno v:
In Information and Computation December 2024 301 Part A
One of the major problems writers and poets face is the writer's block. It is a condition in which an author loses the ability to produce new work or experiences a creative slowdown. The problem is more difficult in the context of poetry than prose,
Externí odkaz:
http://arxiv.org/abs/2107.14587
Autor:
Aravind, N. R., Joglekar, Pushkar S.
We introduce and study the notion of read-$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
Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also give applications and connections to polynomial identity testing. Our
Externí odkaz:
http://arxiv.org/abs/0907.4006