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Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

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Reports tagged with Polynomial Degree:
TR20-002 | 6th January 2020
Sophie Laplante, Reza Naserasr, Anupa Sunny

Sensitivity lower bounds from linear dependencies

Recently, using spectral techniques, H. Huang proved that every subgraph of the hypercube of dimension n induced on more than half the vertices has maximum degree at least the square root of n. Combined with some earlier work, this completed a proof of the sensitivity conjecture. In this work we ... more >>>

TR20-020 | 21st February 2020
Nikhil Mande, Justin Thaler, Shuchen Zhu

Improved Approximate Degree Bounds For $k$-distinctness

An open problem that is widely regarded as one of the most important in quantum query complexity is to resolve the quantum query complexity of the $k$-distinctness function on inputs of size $N$. While the case of $k=2$ (also called Element Distinctness) is well-understood, there is a polynomial gap between ... more >>>

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