Logical Approaches to Computational Barriers

Exploring the computational contribution of a non-constructive combinatorial principle

Speaker:
| Trifon Trifonov |

Author(s): |
Diana Ratiu and Trifon Trifonov |

Slot: |
Array, 11:20-11:40, col. 2 |

The use of classical logic for some combinatoric proofs, as for Ramsey's theorem or Weak K??ig's Lemma, can be localized in the Infinite Pigeon Hole (IPH) principle, stating that any infinite sequence, which is finitely colored, has an infinite monochromatic subsequence. In general, there is no computable functional producing such an infinite subsequence. However, it is possible to extract a program from a corollary proving the classical existence of a finite monochromatic subsequence of any given length. We applied two methods for extraction from classical proofs - the refined A-translation, as proposed by Berger et al., and G??el's Dialectica interpretation. In this talk we will compare the resulting programs and indicate how they reflect the computational content of IPH.

websites: Arnold Beckmann | 2008-05-19 |