Superpolynomial Lower Bounds for General Homogeneous Depth 4 Arithmetic Circuits

In this paper, we prove superpolynomial lower bounds for the class of homogeneous depth 4 arithmetic circuits. We give an explicit polynomial in VNP of degree n in n 2 variables such that any homogeneous depth 4 arithmetic circuit computing it must have size n Ω(loglogn).

[1]  Partha Mukhopadhyay,et al.  Depth-4 Lower Bounds, Determinantal Complexity: A Unified Approach , 2014, STACS.

[2]  Shubhangi Saraf,et al.  Lower Bounds for Depth 4 Homogenous Circuits with Bounded Top Fanin , 2013, Electron. Colloquium Comput. Complex..

[3]  Ran Raz Elusive functions and lower bounds for arithmetic circuits , 2008, STOC '08.

[4]  Leslie G. Valiant,et al.  Fast Parallel Computation of Polynomials Using Few Processors , 1983, SIAM J. Comput..

[5]  Shubhangi Saraf,et al.  On the Power of Homogeneous Depth 4 Arithmetic Circuits , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[6]  Leslie G. Valiant,et al.  Completeness classes in algebra , 1979, STOC.

[7]  Noam Nisan,et al.  Lower bounds on arithmetic circuits via partial derivatives , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[8]  Neeraj Kayal An exponential lower bound for the sum of powers of bounded degree polynomials , 2012, Electron. Colloquium Comput. Complex..

[9]  Noam Nisan,et al.  Lower Bounds for Arithmetic Circuits via Partial Serivatives (Preliminary Version). , 1995, FOCS 1995.

[10]  Nutan Limaye,et al.  Super-polynomial lower bounds for depth-4 homogeneous arithmetic formulas , 2014, STOC.

[11]  Sébastien Tavenas,et al.  Improved bounds for reduction to depth 4 and depth 3 , 2013, Inf. Comput..

[12]  Pascal Koiran,et al.  Arithmetic circuits: The chasm at depth four gets wider , 2010, Theor. Comput. Sci..

[13]  Nutan Limaye,et al.  Lower bounds for depth 4 formulas computing iterated matrix multiplication , 2014, STOC.

[14]  Shubhangi Saraf,et al.  The limits of depth reduction for arithmetic formulas: it's all about the top fan-in , 2013, Electron. Colloquium Comput. Complex..

[15]  Neeraj Kayal,et al.  Approaching the Chasm at Depth Four , 2013, 2013 IEEE Conference on Computational Complexity.

[16]  V. Vinay,et al.  Arithmetic Circuits: A Chasm at Depth Four , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[17]  Neeraj Kayal,et al.  A super-polynomial lower bound for regular arithmetic formulas , 2014, STOC.

[18]  Ran Raz,et al.  Lower Bounds and Separations for Constant Depth Multilinear Circuits , 2008, Computational Complexity Conference.

[19]  Nutan Limaye,et al.  An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.