The Power of Depth 2 Circuits over Algebras

@article{Saha2009ThePO,
  title={The Power of Depth 2 Circuits over Algebras},
  author={Chandan Saha and Ramprasad Saptharishi and Nitin Saxena},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2009},
  volume={16},
  pages={36}
}
We study the problem of polynomial identity testing (PIT) for depth 2 arithmetic circuits over matrix algebra. We show that identity testing of depth 3 (ΣΠΣ) arithmetic circuits over a field F is polynomial time equivalent to identity testing of depth 2 (ΠΣ) arithmetic circuits over U2(F), the algebra of upper-triangular 2× 2 matrices with entries from F. Such a connection is a bit surprising since we also show that, as computational models, ΠΣ circuits over U2(F) are strictly ‘weaker’ than… CONTINUE READING

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