Lower bounds and separations for constant depth multilinear circuits

Ran Raz; Amir Yehudayoff

doi:10.1109/CCC.2008.8

Lower bounds and separations for constant depth multilinear circuits

Ran Raz, Amir Yehudayoff

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

16 Scopus citations

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-depth¹ 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)
Title of host publication	Proceedings - 23rd Annual IEEE Conference on Computational Complexity, CCC 2008
Pages	128-139
Number of pages	12
DOIs	https://doi.org/10.1109/CCC.2008.8
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
ISSN (Print)	1093-0159

Other

Other	23rd Annual IEEE Conference on Computational Complexity, CCC 2008
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

Access to Document

10.1109/CCC.2008.8

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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

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title = "Lower bounds and separations for constant depth multilinear circuits",

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-depth1 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.",

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doi = "10.1109/CCC.2008.8",

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series = "Proceedings of the Annual IEEE Conference on Computational Complexity",

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note = "23rd Annual IEEE Conference on Computational Complexity, CCC 2008 ; Conference date: 23-06-2008 Through 26-06-2008",

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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., 4558817, Proceedings of the Annual IEEE Conference on Computational Complexity, pp. 128-139, 23rd Annual IEEE Conference on Computational Complexity, CCC 2008, College Park, MD, United States, 6/23/08. https://doi.org/10.1109/CCC.2008.8

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AB - 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-depth1 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.

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