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Electronic Colloquium on Computational Complexity

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Reports tagged with gate elimination:
TR16-119 | 1st August 2016
Alexander Golovnev, Edward Hirsch, Alexander Knop, Alexander Kulikov

On the Limits of Gate Elimination

Revisions: 1

Although a simple counting argument shows the existence of Boolean functions of exponential circuit complexity, proving superlinear circuit lower bounds for explicit functions seems to be out of reach of the current techniques. There has been a (very slow) progress in proving linear lower bounds with the latest record of ... more >>>

TR21-023 | 20th February 2021
Jiatu Li, Tianqi Yang

$3.1n - o(n)$ Circuit Lower Bounds for Explicit Functions

Proving circuit lower bounds has been an important but extremely hard problem for decades. Although one may show that almost every function $f:\mathbb{F}_2^n\to\mathbb{F}_2$ requires circuit of size $\Omega(2^n/n)$ by a simple counting argument, it remains unknown whether there is an explicit function (for example, a function in $NP$) not computable ... more >>>

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