An Exponenetioal Lower Bound to the Size of Bounded Depth Frege Proofs of the Pigeonhole Principle.
Jan KrajícekPavel PudlákAlan R. WoodsPublished in: Random Struct. Algorithms (1995)
Keyphrases
- lower bound
- upper bound
- branch and bound algorithm
- branch and bound
- objective function
- running times
- optimal solution
- constant factor
- lower and upper bounds
- theorem proving
- np hard
- bounded treewidth
- memory requirements
- worst case
- upper and lower bounds
- computational complexity
- polynomial size
- formal proofs
- mathematical proofs