ECCC-Report TR11-134https://eccc.weizmann.ac.il/report/2011/134Comments and Revisions published for TR11-134en-usSun, 09 Oct 2011 15:22:57 +0200
Paper TR11-134
| Separating multilinear branching programs and formulas |
Zeev Dvir,
Guillaume Malod,
Sylvain Perifel,
Amir Yehudayoff
https://eccc.weizmann.ac.il/report/2011/134This 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 $n^{\Omega(\log n)}$.
Sun, 09 Oct 2011 15:22:57 +0200https://eccc.weizmann.ac.il/report/2011/134