On the limits of depth reduction at depth 3 over small finite fields

@article{Chillara2017OnTL,
  title={On the limits of depth reduction at depth 3 over small finite fields},
  author={Suryajith Chillara and Partha Mukhopadhyay},
  journal={Inf. Comput.},
  year={2017},
  volume={256},
  pages={35-44}
}
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4 Citations

4 Citations

Citation Type

Citation Type

On the Power of Homogeneous Depth 4 Arithmetic Circuits
TLDR
It is shown that any homogeneous depth 4 circuit computing the (1, 1) entry in the product of n generic matrices of dimension nO(1) must have size nΩ(√n) and the results strengthen previous works in two significant ways.
An exponential lower bound for homogeneous depth-5 circuits over finite fields
TLDR
This paper shows exponential lower bounds for the class of homogeneous depth-$5 circuits over all small finite fields and builds over a tighter analysis of the lower bound of Kumar and Saraf [KS14], the first super-polynomial lower bound for this class for any field.
Lower bounds for bounded depth arithmetic circuits
TLDR
A strong hierarchy theorem for bottom fan-in for homogeneous depth-4 circuits, a superpolynomial lower bound for homogeneity depth-5 circuits over finite fields, and some results indicating that the parameters for depth reduction to homogeneous Depth 4 circuits might be close to optimal in a fairly strong sense.
On the Power of Homogeneous Depth 4 Arithmetic Circuits
  • SIAM J. Comput.
  • 2017

References

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On the Power of Homogeneous Depth 4 Arithmetic Circuits
TLDR
It is shown that any homogeneous depth 4 circuit computing the (1, 1) entry in the product of n generic matrices of dimension nO(1) must have size nΩ(√n) and the results strengthen previous works in two significant ways.
Lower bounds for depth 4 formulas computing iterated matrix multiplication
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It is shown that any multilinear homogeneous depth 4 arithmetic formula computing the product of d generic matrices of size n × n, IMMn,d, has size nΩ(√d) as long as d = nO(1), improving the result of Nisan and Wigderson (Computational Complexity, 1997).
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We show that, over Q, if an n-variate polynomial of degree d = n<sup>O(1)</sup> is computable by an arithmetic circuit of size s (respectively by an arithmetic branching program of size s) then it…
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Depth-4 Lower Bounds, Determinantal Complexity: A Unified Approach
TLDR
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Diagonal Circuit Identity Testing and Lower Bounds
In this paper we give the first deterministic polynomial time algorithm for testing whether a diagonaldepth-3 circuit C(x 1 ,...,x n ) (i.e. Cis a sum of powers of linear functions) is zero. We also…
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