Basic proof theory
On the proof complexity of deep inference
ACM Transactions on Computational Logic (TOCL)
Deep inference and its normal form of derivations
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Complexity of deep inference via atomic flows
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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It has recently been shown that cut-free deep inference systems exhibit an exponential speed-up over cut-free sequent systems, in terms of proof size. While this is good for proof complexity, there remains the problem of typically high proof search non-determinism induced by the deep inference methodology: the higher the depth of inference, the higher the non-determinism. In this work we improve on the proof search side by demonstrating that, for propositional logic, the same exponential speed-up in proof size can be obtained in bounded-depth cut-free systems. These systems retain the top-down symmetry of deep inference, but can otherwise be designed at the same depth level of sequent systems. As a result the non-determinism arising from the choice of rules at each stage of a proof is smaller than that of unbounded deep inference, while still giving access to the short proofs of deep inference.