| Presentation | 2009-10-16 Breaking the Rectangle Bound Barrier against Formula Size Lower Bounds Kenya UENO, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | 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 as a quasi-additive bound and the Sherali-Adams bound. While the Sherali-Adams 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. We also discuss structure of the universal relation towards its matching bound because we can derive a formula size lower bound of any Boolean function from a solution of the quasi-additive bound for the universal relation. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Formal Complexity Measures / Formula Size / Lift-and-Project Methods / Linear Programming |
| Paper # | COMP2009-38 |
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| Conference Information | |
| Committee | COMP |
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| Conference Date | 2009/10/9(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Paper Information | |
| Registration To | Theoretical Foundations of Computing (COMP) |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Breaking the Rectangle Bound Barrier against Formula Size Lower Bounds |
| Sub Title (in English) | |
| Keyword(1) | Formal Complexity Measures |
| Keyword(2) | Formula Size |
| Keyword(3) | Lift-and-Project Methods |
| Keyword(4) | Linear Programming |
| 1st Author's Name | Kenya UENO |
| 1st Author's Affiliation | Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo() |
| Date | 2009-10-16 |
| Paper # | COMP2009-38 |
| Volume (vol) | vol.109 |
| Number (no) | 235 |
| Page | pp.pp.- |
| #Pages | 8 |
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