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We present a deterministic polynomial-time algorithm that determines whether an input number n is prime or composite. â€œThe problem of distinguishing prime numbers from composite numbers and ofâ€¦ (More)

- Neeraj Kayal, Nitin Saxena
- IEEE Conference on Computational Complexity
- 2006

- Neeraj Kayal
- Electronic Colloquium on Computational Complexity
- 2011

An m-variate polynomial f is said to be an affine projection of some n-variate polynomial g if there exists an nÃ—m matrix A and an n-dimensional vector b such that f(x) = g(Ax + b). In other words,â€¦ (More)

- Ankit Gupta, Pritish Kamath, Neeraj Kayal, Ramprasad Saptharishi
- 2013 IEEE Conference on Computational Complexity
- 2013

Agrawal and Vinay [2008], Koiran [2012], and Tavenas [2013] have recently shown that an exp (Ï‰(âˆšn log n)) lower bound for depth four homogeneous circuits computing the permanent with bottom layer ofâ€¦ (More)

- Neeraj Kayal, Shubhangi Saraf
- 2009 50th Annual IEEE Symposium on Foundations ofâ€¦
- 2009

We study depth three arithmetic circuits with bounded top fanin. We give the first deterministic polynomial time blackbox identity test for depth three circuits with bounded top fanin over the fieldâ€¦ (More)

- Ankit Gupta, Pritish Kamath, Neeraj Kayal, Ramprasad Saptharishi
- 2013 IEEE 54th Annual Symposium on Foundations ofâ€¦
- 2013

We show that, over Q, if an n-variate polynomial of degree d = n<sup>O(1)</sup> is computable by an arithmetic circuit of size s (respectively by an arithmetic branching program of size s) then itâ€¦ (More)

- Xi Chen, Neeraj Kayal, Avi Wigderson
- 2011

How complex is a given multivariate polynomial? The main point of this survey is that one can learn a great deal about the structure and complexity of polynomials by studying (some of) their partialâ€¦ (More)

- Ankit Gupta, Pritish Kamath, Neeraj Kayal, Ramprasad Saptharishi
- Electronic Colloquium on Computational Complexity
- 2012

Agrawal and Vinay [AV08] have recently shown that an exponential lower bound for depth four homogeneous circuits with bottom layer of Ã— gates having sublinear fanin translates to an exponential lowerâ€¦ (More)

- Neeraj Kayal
- SODA
- 2011

We consider the following computational problem. Let F be a field. Given two <i>n</i>-variate polynomials <i>f</i>(<i>x</i><sub>1</sub>,.., <i>x</i><sub><i>n</i></sub>) andâ€¦ (More)

- Neeraj Kayal
- Electronic Colloquium on Computational Complexity
- 2012

In this work we consider representations of multivariate polynomials in F[x] of the form f(x) = Q1(x)1 +Q2(x)2 + . . .+Qs(x) , where the eiâ€™s are positive integers and the Qiâ€™s are arbitaryâ€¦ (More)