eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-07-04
36:1
36:13
10.4230/LIPIcs.ICALP.2018.36
article
A Quadratic Size-Hierarchy Theorem for Small-Depth Multilinear Formulas
Chillara, Suryajith
1
Limaye, Nutan
1
Srinivasan, Srikanth
2
Department of CSE, IIT Bombay, Mumbai, India
Department of Mathematics, IIT Bombay, Mumbai, India
We show explicit separations between the expressive powers of multilinear formulas of small-depth and all polynomial sizes.
Formally, for any s = s(n) = n^{O(1)} and any delta>0, we construct explicit families of multilinear polynomials P_n in F[x_1,...,x_n] that have multilinear formulas of size s and depth three but no multilinear formulas of size s^{1/2-delta} and depth o(log n/log log n).
As far as we know, this is the first such result for an algebraic model of computation.
Our proof can be viewed as a derandomization of a lower bound technique of Raz (JACM 2009) using epsilon-biased spaces.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol107-icalp2018/LIPIcs.ICALP.2018.36/LIPIcs.ICALP.2018.36.pdf
Algebraic circuit complexity
Multilinear formulas
Lower Bounds