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Asymptotic Cyclic Expansion and Bridge Groups of Formal Proofs

✍ Scribed by A. Carbone

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 515 KB
Volume: 242
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8700

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✦ Synopsis

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.

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