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Electronic Colloquium on Computational Complexity

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All reports by Author Deepanshu Kush:

TR23-212 | 26th December 2023
Prerona Chatterjee, Deepanshu Kush, Shubhangi Saraf, Amir Shpilka

Exponential Lower Bounds Against Sums of ROABPs

Revisions: 2

In this paper, we prove the first super-polynomial and, in fact, exponential lower bound for the model of sum of read-once oblivious algebraic branching programs (ROABPs). In particular, we give an explicit polynomial such that any sum of ROABPs
(equivalently, sum of *ordered* set-multilinear branching programs, each with a ... more >>>

TR23-017 | 21st February 2023
Deepanshu Kush, Shubhangi Saraf

Near-Optimal Set-Multilinear Formula Lower Bounds

The seminal work of Raz (J. ACM 2013) as well as the recent breakthrough results by Limaye, Srinivasan, and Tavenas (FOCS 2021, STOC 2022) have demonstrated a potential avenue for obtaining lower bounds for general algebraic formulas, via strong enough lower bounds for set-multilinear formulas.

In this paper, we make ... more >>>

TR22-064 | 2nd May 2022
Deepanshu Kush, Shubhangi Saraf

Improved Low-Depth Set-Multilinear Circuit Lower Bounds

In this paper, we prove strengthened lower bounds for constant-depth set-multilinear formulas. More precisely, we show that over any field, there is an explicit polynomial $f$ in VNP defined over $n^2$ variables, and of degree $n$, such that any product-depth $\Delta$ set-multilinear formula computing $f$ has size at least $n^{\Omega ... more >>>

TR20-061 | 28th April 2020
Deepanshu Kush, Benjamin Rossman

Tree-depth and the Formula Complexity of Subgraph Isomorphism

For a fixed "pattern" graph $G$, the $\textit{colored}$ $G\textit{-subgraph isomorphism problem}$ (denoted $\mathrm{SUB}(G)$) asks, given an $n$-vertex graph $H$ and a coloring $V(H) \to V(G)$, whether $H$ contains a properly colored copy of $G$. The complexity of this problem is tied to parameterized versions of $\mathit{P}$ ${=}?$ $\mathit{NP}$ and $\mathit{L}$ ... 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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