### Abstract

We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multilinear, if the polynomial computed by each of its gates is multilinear). We also prove a super-polynomial separation between the size of product-depth^{1} d and product-depth d+1 multilinear circuits (where d is constant). That is, there exists a polynomial f such that • There exists a multilinear circuit of pro duct-depth d+1 and of polynomial size computing f. • Every multilinear circuit of product-depth d computing f has super-polynomial size.

Original language | English (US) |
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Title of host publication | Proceedings - 23rd Annual IEEE Conference on Computational Complexity, CCC 2008 |

Pages | 128-139 |

Number of pages | 12 |

DOIs | |

State | Published - Sep 23 2008 |

Externally published | Yes |

Event | 23rd Annual IEEE Conference on Computational Complexity, CCC 2008 - College Park, MD, United States Duration: Jun 23 2008 → Jun 26 2008 |

### Publication series

Name | Proceedings of the Annual IEEE Conference on Computational Complexity |
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ISSN (Print) | 1093-0159 |

### Other

Other | 23rd Annual IEEE Conference on Computational Complexity, CCC 2008 |
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Country | United States |

City | College Park, MD |

Period | 6/23/08 → 6/26/08 |

### All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Computational Mathematics

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## Cite this

Raz, R., & Yehudayoff, A. (2008). Lower bounds and separations for constant depth multilinear circuits. In

*Proceedings - 23rd Annual IEEE Conference on Computational Complexity, CCC 2008*(pp. 128-139). [4558817] (Proceedings of the Annual IEEE Conference on Computational Complexity). https://doi.org/10.1109/CCC.2008.8