Corpus ID: 208309794

A Quadratic Lower Bound for Algebraic Branching Programs

@article{Chatterjee2019AQL,
title={A Quadratic Lower Bound for Algebraic Branching Programs},
author={Prerona Chatterjee and Mrinal Kumar and Adrian She and Ben lee Volk},
journal={Electronic Colloquium on Computational Complexity (ECCC)},
year={2019},
volume={26},
pages={170}
}
• Prerona Chatterjee, +1 author Ben lee Volk
• Published 2019
• Computer Science, Mathematics
• Electronic Colloquium on Computational Complexity (ECCC)
• We show that any Algebraic Branching Program (ABP) computing the polynomial $\sum_{i = 1}^n x_i^n$ has at least $\Omega(n^2)$ vertices. This improves upon the lower bound of $\Omega(n\log n)$, which follows from the classical result of Baur and Strassen [Str73, BS83], and extends the results in [K19], which showed a quadratic lower bound for \emph{homogeneous} ABPs computing the same polynomial. Our proof relies on a notion of depth reduction which is reminiscent of similar statements in the… CONTINUE READING

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References

Publications referenced by this paper.
SHOWING 1-10 OF 31 REFERENCES

A quadratic lower bound for homogeneous algebraic branching programs

• Mrinal Kumar
• Mathematics, Computer Science
• Electronic Colloquium on Computational Complexity
• 2017

A Lower Bound for the Formula Size of Rational Functions

• K. Kalorkoti
• Mathematics, Computer Science
• SIAM J. Comput.
• 1985

Arithmetic Circuits: A Chasm at Depth 3

• Mathematics, Computer Science
• SIAM J. Comput.
• 2016

Depth-3 arithmetic circuits over fields of characteristic zero

• Computer Science, Mathematics
• computational complexity
• 2001

Balancing Syntactically Multilinear Arithmetic Circuits

• Computer Science, Mathematics
• computational complexity
• 2008

Arithmetic Circuits: A survey of recent results and open questions

• Computer Science
• Foundations and Trends in Theoretical Computer Science
• 2010

On sparse graphs with dense long paths.

• Mathematics
• 1975
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