Breaking the Rectangle Bound Barrier against Formula Size Lower Bounds

Karchmer, Kushilevitz and Nisan formulated the formula size problem as an integer programming problem called the rectangle bound and introduced a technique called the LP bound, which gives a formula size lower bound by showing a feasible solution of the dual problem of its LP-relaxation. As extensions of the LP bound, we introduce novel general techniques proving formula size lower bounds, named a quasi-additive bound and the Sherali-Adams bound. While the SheraliAdams bound is potentially strong enough to give a lower bound matching to the rectangle bound, we prove that the quasi-additive bound can surpass the rectangle bound.

• Type: Journal
• Year: 2010
• Where: MFCS
• Authors: Kenya Ueno
• Keywords: Formula Size, Lower Bound, MFCS 2010, Quasi-additive Bound, Theoretical Computer Science