Volume 2 (2006)
Article 6 pp. 121-135
Separation of Multilinear Circuit and Formula Size
Received: September 30, 2005
Revised: March 4, 2006
Published: May 2, 2006
Revised: March 4, 2006
Published: May 2, 2006
Keywords: algebraic complexity, arithmetic circuits, log-depth, multilinear polynomials, lower bounds, separation of complexity classes
Categories: complexity theory, lower bounds, circuits, arithmetic circuits, formulas, arithmetic formulas, complexity classes, separation of complexity classes, polynomials
ACM Classification: F.2.2, F.1.3, F.1.2, G.2.0
AMS Classification: 68Q15, 68Q17, 68Q25, 94C05
Abstract: [Plain Text Version]
An arithmetic circuit or formula is multilinear if the polynomial computed
at each of its wires is multilinear. We give an explicit polynomial
f(x1,...,xn) with coefficients in
{0,1} such that over any field:
- f can be computed by a polynomial-size multilinear circuit of depth O(log2n).
- Any multilinear formula for f is of size nΩ(log n).
Licensed under a Creative Commons License