Exponential lower bounds for the pigeonhole principle
Computational Complexity
Basic proof theory
An exponential lower bound to the size of bounded depth Frege proofs of the Pigeonhole Principle
Random Structures & Algorithms
On the proof complexity of deep inference
ACM Transactions on Computational Logic (TOCL)
Proof Complexity of the Cut-free Calculus of Structures
Journal of Logic and Computation
On the proof complexity of cut-free bounded deep inference
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
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We consider the fragment of deep inference free of compression mechanisms and compare its proof complexity to other systems, utilising ‘atomic flows' to examine size of proofs. Results include a simulation of Resolution and dag-like cut-free Gentzen, as well as a separation from bounded-depth Frege.