## Section: New Results

### Cut-elimination in classical logic

Participant : Stefan Hetzl.

A central research topic of the team are the connections between proof theory and computation. A proof-theoretic method which is often used for modeling computational systems is cut-elimination. The computational aspects of this procedure are rather well understood for intuitionistic and linear logic while the situation in classical logic is less satisfactory. [26] shows that in the general case the number of possible computational interpretations of a classical proof increases as strongly as its computational power and thus provides a lower bound on the set computations encoded by proof. [46] on the other hand considers proof in classical first-order logic and Peano arithmetic and derives an upper bound which is characterized by a regular tree grammar. This grammar can be used as alternative algorithm for computing cut-free proofs and is therefore a contribution to the reduction of syntax in proof theory.