Kayal, Neeraj and Limaye, Nutan and Saha, Chandan and Srinivasan, Srikanth
(2014)
*An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas.*
In: 55th Annual IEEE Symposium on Foundations of Computer Science (FOCS), OCT 18-21, 2014, Microsoft Res New England, Philadelphia, PA, pp. 61-70.

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## Abstract

We show here a 2(Omega(root d.log N)) size lower bound for homogeneous depth four arithmetic formulas. That is, we give an explicit family of polynomials of degree d on N variables (with N = d(3) in our case) with 0, 1-coefficients such that for any representation of a polynomial f in this family of the form f = Sigma(i) Pi(j) Q(ij), where the Q(ij)'s are homogeneous polynomials (recall that a polynomial is said to be homogeneous if all its monomials have the same degree), it must hold that Sigma(i,j) (Number of monomials of Q(ij)) >= 2(Omega(root d.log N)). The above mentioned family, which we refer to as the Nisan-Wigderson design-based family of polynomials, is in the complexity class VNP. Our work builds on the recent lower bound results 1], 2], 3], 4], 5] and yields an improved quantitative bound as compared to the quasi-polynomial lower bound of 6] and the N-Omega(log log (N)) lower bound in the independent work of 7].

Item Type: | Conference Proceedings |
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Additional Information: | Copy right for this article belongs to the IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA |

Keywords: | Arithmetic circuits; shifted partial derivatives; lower bounds |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Depositing User: | Id for Latest eprints |

Date Deposited: | 06 Jan 2016 05:44 |

Last Modified: | 06 Jan 2016 05:44 |

URI: | http://eprints.iisc.ac.in/id/eprint/53069 |

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