## Towards an algebraic natural proofs barrier via polynomial identity testing

- Joshua A. Grochow, Mrinal Kumar, Michael E. Saks, Shubhangi Saraf
- Electronic Colloquium on Computational Complexity
- 2017

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@inproceedings{Forbes2017SuccinctHS, title={Succinct Hitting Sets and Barriers to Proving Algebraic Circuits Lower Bounds}, author={Michael A. Forbes and Amir Shpilka and Ben lee Volk}, booktitle={Electronic Colloquium on Computational Complexity}, year={2017} }

- Published 2017 in Electronic Colloquium on Computational Complexity
DOI:10.1145/3055399.3055496

We formalize a framework of algebraically natural lower bounds for algebraic circuits. Just as with the natural proofs notion of Razborov and Rudich for boolean circuit lower bounds, our notion of algebraically natural lower bounds captures nearly all lower bound techniques known. However, unlike the boolean setting, there has been no concrete evidence demonstrating that this is a barrier to obtaining super-polynomial lower bounds for general algebraic circuits, as there is little understanding… CONTINUE READING