Matrix identities and the pigeonhole principle
โ Scribed by Michael Soltys; Alasdair Urquhart
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 83 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0933-5846
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The exact complexity of the weak pigeonhole principle is an old and fundamental problem in proof complexity. Using a diagonalization argument, J. B. Paris et al. (J. Symbolic Logic 53 (1988), 1235-1244) showed how to prove the weak pigeonhole principle with bounded-depth, quasipolynomialsize proofs.
## Abstract It is well known that __S__ ^1^~2~ cannot prove the injective weak pigeonhole principle for polynomial time functions unless RSA is insecure. In this note we investigate the provability of the surjective (dual) weak pigeonhole principle in __S__ ^1^~2~ for provably weaker function class
We bring together some facts about the weak pigeonhole principle (WPHP) from bounded arithmetic, complexity theory, cryptography and abstract model theory. We characterize the models of arithmetic in which WPHP fails as those which are determined by an initial segment and prove a conditional separat