All reports by Author Vaibhav Krishan:

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TR23-111
| 29th July 2023
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Vaibhav Krishan#### $\mathit{MidBit}^+$, Torus Polynomials and Non-classical Polynomials: Equivalences for $\mathit{ACC}$ Lower Bounds

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TR21-031
| 3rd March 2021
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Vaibhav Krishan#### Upper Bound for Torus Polynomials

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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

Vaibhav Krishan

We give a conversion from non-classical polynomials to $\mathit{MidBit}^+$ circuits and vice-versa. This conversion, along with previously known results, shows that torus polynomials, non-classical polynomials and $\mathit{MidBit}^+$ circuits can all be converted to each other. Therefore lower bounds against any of these models lead to lower bounds against all three ... more >>>

Vaibhav Krishan

We prove that all functions that have low degree torus polynomials approximating them with small error also have $MidBit^+$ circuits computing them. This serves as a partial converse to the result that all $ACC$ functions have low degree torus polynomials approximating them with small error, by Bhrushundi, Hosseini, Lovett and ... 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 >>>