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Electronic Colloquium on Computational Complexity

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All reports by Author Vaibhav Krishan:

TR23-111 | 29th July 2023
Vaibhav Krishan

$\mathit{MidBit}^+$, Torus Polynomials and Non-classical Polynomials: Equivalences for $\mathit{ACC}$ Lower Bounds

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 >>>

TR21-031 | 3rd March 2021
Vaibhav Krishan

Upper Bound for Torus Polynomials

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 >>>

TR18-162 | 16th September 2018
Swapnam Bajpai, Vaibhav Krishan, Deepanshu Kush, Nutan Limaye, Srikanth Srinivasan

A #SAT Algorithm for Small Constant-Depth Circuits with PTF gates

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 >>>

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