Neeraj Kayal, Nutan Limaye, Chandan Saha, Srikanth Srinivasan

We show here a $2^{\Omega(\sqrt{d} \cdot \log N)}$ size lower bound for homogeneous depth four arithmetic formulas. That is, we give

an explicit family of polynomials of degree $d$ on $N$ variables (with $N = d^3$ in our case) with $0, 1$-coefficients such that

for any representation of ...
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HervĂ© Fournier, Nutan Limaye, Srikanth Srinivasan, SĂ©bastien Tavenas

Proving explicit lower bounds on the size of algebraic formulas is a long-standing open problem in the area of algebraic complexity theory. Recent results in the area (e.g. a lower bound against constant-depth algebraic formulas due to Limaye, Srinivasan, and Tavenas (FOCS 2021)) have indicated a way forward for attacking ... more >>>