Abstract not found

Formal proofs, even simple ones, may hide an unexpected intricate combinatorics. We define a new combinatorial invariant, the bridge group of a proof, which encodes the cyclic structure of proofs in the sequent calculus. We compute the bridge groups of two infinite families of proofs and identify them with the Baumslag–Solitar and Gersten groups. We observe that the distortion of cyclic subgroups in these groups equals the asymptotic growth of the procedure of elimination of lemmas from the proofs. © 2001 Academic Press Key Words: formal proofs; logical flow graphs; cut elimination; bridge groups; Baumslag–Solitar groups; Gersten groups.

Streams are acyclic directed subgraphs of the logical flow graph of a proof and represent bundles of paths with the same origin and the same end. Streams can be described with a natural algebraic formalism which allows to explain in algebraic terms the evolution of proofs during cutelimination. In our approach, "logic" is often forgotten and combinatorial properties of graphs are taken into account to explain logical phenomena.

This paper is motivated by questions of complexity and combinatorics of proofs in the sequent calculus. We shall pay particular attention to the role that symmetry plays in these questions.. We want to