Summary: On the Computational Complexity of Cut-Reduction
Klaus Aehlig Arnold Beckmann
Department of Computer Science
Singleton Park, Swansea SA2 8PP, UK
Using appropriate notation systems for proofs, cut-
reduction can often be rendered feasible on these notations.
Explicit bounds can be given. Developing a suitable no-
tation system for Bounded Arithmetic, and applying these
bounds, all the known results on definable functions of cer-
tain such theories can be reobtained in a uniform way.
Since Gentzen's invention of the "Logik Kalk¨ul" LK and
his proof of the "Hauptsatz" [10, 11], cut-elimination has
been a topic of almost any paper on proof theory. Mints'
invention of continuous normalisation [14, 13] isolates op-
erational aspects of normalisation, that is the manipulations
on (infinitary) propositional derivations. These operational