@inproceedings{31f41877813a49dea519e5378be8c5b7,

title = "Separating multilinear branching programs and formulas",

abstract = "This work deals with the power of linear algebra in the context of multilinear computation. By linear algebra we mean algebraic branching programs (ABPs) which are known to be computationally equivalent to two basic tools in linear algebra: iterated matrix multiplication and the determinant. We compare the computational power of multilinear ABPs to that of multilinear arithmetic formulas, and prove a tight super-polynomial separation between the two models. Specifically, we describe an explicit n-variate polynomial F that is computed by a linear-size multilinear ABP but every multilinear formula computing F must be of size n Ω(log n).",

keywords = "algebraic branching programs, arithmetic circuits, arithmetic formulas, multilinear computations, polynomials",

author = "Zeev Dvir and Guillaume Malod and Sylvain Perifel and Amir Yehudayoff",

year = "2012",

doi = "10.1145/2213977.2214034",

language = "English (US)",

isbn = "9781450312455",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

pages = "615--623",

booktitle = "STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing",

note = "44th Annual ACM Symposium on Theory of Computing, STOC '12 ; Conference date: 19-05-2012 Through 22-05-2012",

}