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Electronic Colloquium on Computational Complexity

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All reports by Author Nikhil Gupta:

TR19-042 | 18th March 2019
Ankit Garg, Nikhil Gupta, Neeraj Kayal, Chandan Saha

Determinant equivalence test over finite fields and over $\mathbf{Q}$

The determinant polynomial $Det_n(\mathbf{x})$ of degree $n$ is the determinant of a $n \times n$ matrix of formal variables. A polynomial $f$ is equivalent to $Det_n$ over a field $\mathbf{F}$ if there exists a $A \in GL(n^2,\mathbf{F})$ such that $f = Det_n(A \cdot \mathbf{x})$. Determinant equivalence test over $\mathbf{F}$ is ... more >>>

TR18-164 | 18th September 2018
Nikhil Gupta, Chandan Saha

On the symmetries of design polynomials

Revisions: 1

In a Nisan-Wigderson design polynomial (in short, a design polynomial), the gcd of every pair of monomials has a low degree. A useful example of such a polynomial is the following:
$$\text{NW}_{d,k}(\mathbf{x}) = \sum_{h \in \mathbb{F}_d[z], ~\deg(h) \leq k}{~~~~\prod_{i = 0}^{d-1}{x_{i, h(i)}}},$$
where $d$ is a prime, $\mathbb{F}_d$ is the ... more >>>

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