All reports by Author Srikanth Srinivasan:

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TR19-138
| 6th October 2019
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Srikanth Srinivasan, Utkarsh Tripathi, S Venkitesh#### On the Probabilistic Degrees of Symmetric Boolean functions

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TR18-207
| 5th December 2018
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Siddharth Bhandari, Prahladh Harsha, Tulasimohan Molli, Srikanth Srinivasan#### On the Probabilistic Degree of OR over the Reals

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TR18-162
| 16th September 2018
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Swapnam Bajpai, Vaibhav Krishan, Deepanshu Kush, Nutan Limaye, Srikanth Srinivasan#### A #SAT Algorithm for Small Constant-Depth Circuits with PTF gates

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TR18-062
| 7th April 2018
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Suryajith Chillara, Christian Engels, Nutan Limaye, Srikanth Srinivasan#### A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits

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TR17-156
| 15th October 2017
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Suryajith Chillara, Nutan Limaye, Srikanth Srinivasan#### Small-depth Multilinear Formula Lower Bounds for Iterated Matrix Multiplication, with Applications

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TR17-013
| 23rd January 2017
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Abhishek Bhrushundi, Prahladh Harsha, Srikanth Srinivasan#### On polynomial approximations over $\mathbb{Z}/2^k\mathbb{Z}$

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TR16-143
| 15th September 2016
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Nikhil Balaji, Nutan Limaye, Srikanth Srinivasan#### An Almost Cubic Lower Bound for $\Sigma\Pi\Sigma$ Circuits Computing a Polynomial in VP

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TR15-118
| 23rd July 2015
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Hervé Fournier, Nutan Limaye, Meena Mahajan, Srikanth Srinivasan#### The shifted partial derivative complexity of Elementary Symmetric Polynomials

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TR15-022
| 9th February 2015
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Nutan Limaye, Guillaume Malod, Srikanth Srinivasan#### Lower bounds for non-commutative skew circuits

Revisions: 1

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TR14-005
| 14th January 2014
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Neeraj Kayal, Nutan Limaye, Chandan Saha, Srikanth Srinivasan#### An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas

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TR13-167
| 28th November 2013
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Venkatesan Guruswami, Prahladh Harsha, Johan Håstad, Srikanth Srinivasan, Girish Varma#### Super-polylogarithmic hypergraph coloring hardness via low-degree long codes

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TR12-158
| 14th November 2012
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Aditya Bhaskara, Devendra Desai, Srikanth Srinivasan#### Optimal Hitting Sets for Combinatorial Shapes

Srikanth Srinivasan, Utkarsh Tripathi, S Venkitesh

The probabilistic degree of a Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is defined to be the smallest $d$ such that there is a random polynomial $\mathbf{P}$ of degree at most $d$ that agrees with $f$ at each point with high probability. Introduced by Razborov (1987), upper and lower bounds on probabilistic degrees ... more >>>

Siddharth Bhandari, Prahladh Harsha, Tulasimohan Molli, Srikanth Srinivasan

We study the probabilistic degree over reals of the OR function on $n$ variables. For an error parameter $\epsilon$ in (0,1/3), the $\epsilon$-error probabilistic degree of any Boolean function $f$ over reals is the smallest non-negative integer $d$ such that the following holds: there exists a distribution $D$ of polynomials ... more >>>

Swapnam Bajpai, Vaibhav Krishan, Deepanshu Kush, Nutan Limaye, Srikanth Srinivasan

We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of constant-degree polynomials), counts the number of satisfying assignments to $C$ in significantly better than ... more >>>

Suryajith Chillara, Christian Engels, Nutan Limaye, Srikanth Srinivasan

We study the size blow-up that is necessary to convert an algebraic circuit of product-depth $\Delta+1$ to one of product-depth $\Delta$ in the multilinear setting.

We show that for every positive $\Delta = \Delta(n) = o(\log n/\log \log n),$ there is an explicit multilinear polynomial $P^{(\Delta)}$ on $n$ variables that ... more >>>

Suryajith Chillara, Nutan Limaye, Srikanth Srinivasan

The complexity of Iterated Matrix Multiplication is a central theme in Computational Complexity theory, as the problem is closely related to the problem of separating various complexity classes within $\mathrm{P}$. In this paper, we study the algebraic formula complexity of multiplying $d$ many $2\times 2$ matrices, denoted $\mathrm{IMM}_{d}$, and show ... more >>>

Abhishek Bhrushundi, Prahladh Harsha, Srikanth Srinivasan

We study approximation of Boolean functions by low-degree polynomials over the ring $\mathbb{Z}/2^k\mathbb{Z}$. More precisely, given a Boolean function F$:\{0,1\}^n \rightarrow \{0,1\}$, define its $k$-lift to be F$_k:\{0,1\}^n \rightarrow \{0,2^{k-1}\}$ by $F_k(x) = 2^{k-F(x)}$ (mod $2^k$). We consider the fractional agreement (which we refer to as $\gamma_{d,k}(F)$) of $F_k$ with ... more >>>

Nikhil Balaji, Nutan Limaye, Srikanth Srinivasan

In this note, we prove that there is an explicit polynomial in VP such that any $\Sigma\Pi\Sigma$ arithmetic circuit computing it must have size at least $n^{3-o(1)}$. Up to $n^{o(1)}$ factors, this strengthens a recent result of Kayal, Saha and Tavenas (ICALP 2016) which gives a polynomial in VNP with ... more >>>

Hervé Fournier, Nutan Limaye, Meena Mahajan, Srikanth Srinivasan

We continue the study of the shifted partial derivative measure, introduced by Kayal (ECCC 2012), which has been used to prove many strong depth-4 circuit lower bounds starting from the work of Kayal, and that of Gupta et al. (CCC 2013).

We show a strong lower bound on the dimension ... more >>>

Nutan Limaye, Guillaume Malod, Srikanth Srinivasan

Nisan (STOC 1991) exhibited a polynomial which is computable by linear sized non-commutative circuits but requires exponential sized non-commutative algebraic branching programs. Nisan's hard polynomial is in fact computable by linear sized skew circuits (skew circuits are circuits where every multiplication gate has the property that all but one of ... more >>>

Neeraj Kayal, Nutan Limaye, Chandan Saha, Srikanth Srinivasan

We show here a $2^{\Omega(\sqrt{d} \cdot \log N)}$ size lower bound for homogeneous depth four arithmetic formulas. That is, we give

an explicit family of polynomials of degree $d$ on $N$ variables (with $N = d^3$ in our case) with $0, 1$-coefficients such that

for any representation of ...
more >>>

Venkatesan Guruswami, Prahladh Harsha, Johan Håstad, Srikanth Srinivasan, Girish Varma

We prove improved inapproximability results for hypergraph coloring using the low-degree polynomial code (aka, the “short code” of Barak et. al. [FOCS 2012]) and the techniques proposed by Dinur and Guruswami [FOCS 2013] to incorporate this code for inapproximability results.

In particular, we prove quasi-NP-hardness of the following problems on ... more >>>

Aditya Bhaskara, Devendra Desai, Srikanth Srinivasan

We consider the problem of constructing explicit Hitting sets for Combinatorial Shapes, a class of statistical tests first studied by Gopalan, Meka, Reingold, and Zuckerman (STOC 2011). These generalize many well-studied classes of tests, including symmetric functions and combinatorial rectangles. Generalizing results of Linial, Luby, Saks, and Zuckerman (Combinatorica 1997) ... more >>>