# Succinct hitting sets and barriers to proving algebraic circuits lower bounds

@article{Forbes2017SuccinctHS, title={Succinct hitting sets and barriers to proving algebraic circuits lower bounds}, author={Michael A. Forbes and Amir Shpilka and Ben lee Volk}, journal={Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing}, year={2017} }

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

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VIEW 5 EXCERPTS

CITES BACKGROUND & RESULTS

HIGHLY INFLUENCED

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VIEW 2 EXCERPTS

CITES METHODS

HIGHLY INFLUENCED

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VIEW 6 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

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VIEW 1 EXCERPT

CITES BACKGROUND

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VIEW 2 EXCERPTS

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 10 REFERENCES

## Natural proofs versus derandomization

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Deterministic extractors for a ne sources over large elds

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

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

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Unifying Known Lower Bounds via Geometric Complexity Theory

VIEW 9 EXCERPTS

HIGHLY INFLUENTIAL

## Arithmetic natural proofs theory is sought

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Lower Bounds and Separations for Constant Depth Multilinear Circuits

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL

## Randomness efficient identity testing of multivariate polynomials

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## Fast Probabilistic Algorithms for Verification of Polynomial Identities

VIEW 12 EXCERPTS

HIGHLY INFLUENTIAL

## Probabilistic algorithms for sparse polynomials. In Symbolic and Algebraic Computation, EUROSAM ’79

VIEW 12 EXCERPTS

HIGHLY INFLUENTIAL

## A Probabilistic Remark on Algebraic Program Testing

VIEW 12 EXCERPTS

HIGHLY INFLUENTIAL