theoretical-computer-science / Algebraic complexity

Lower Bounds for the Permanent in Arithmetic Circuits

How large must arithmetic circuits and formulas computing the $n \times n$ permanent be? New lower bounds include an arithmetic-formula bound of order $n^4/\log n$, far beyond the quadratic barrier that stood for decades.

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How large must arithmetic circuits and formulas computing the $n \times n$ permanent be? New lower bounds include an arithmetic-formula bound of order $n^4/\log n$, far beyond the quadratic barrier that stood for decades.

an n^4/log n formula lower bound; VP vs VNP remains wide open

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