Abstract
We prove that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length Ω2(2nε), (for some global constant ε > 0). One corollary is that a certain prepositional formulation of the statement NP ⊄ P/ poly does not have short Resolution proofs.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 115-138 |
| Number of pages | 24 |
| Journal | Journal of the ACM |
| Volume | 51 |
| Issue number | 2 |
| DOIs | |
| State | Published - Mar 2004 |
| Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Software
- Control and Systems Engineering
- Information Systems
- Hardware and Architecture
- Artificial Intelligence
Keywords
- Computational complexity
- Lower bounds
- P different than NP
- Prepositional logic
- Proof complexity