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On the computational complexity of cutreduction

Summary: On the computational complexity of
Klaus Aehlig Arnold Beckmann
Department of Computer Science
University of Wales Swansea
Singleton Park, Swansea SA2 8PP, UK
February 15, 2009
Using appropriate notation systems for proofs, cut­reduction can often
be rendered feasible on these notations. Explicit bounds can be given. De­
veloping a suitable notation system for Bounded Arithmetic, and applying
these bounds, all the known results on definable functions of certain such
theories can be reobtained in a uniform way.
1 Introduction and Related Work
Since Gentzen's invention of the ``Logik Kalk˜ul'' LK and the proof of his ``Haupt­
satz'' [Gen35a, Gen35b], cut­elimination has been studied in many papers on
proof theory. Mints' invention of continuous normalisation [Min78, KMS75]
isolates operational aspects of normalisation, that is, the manipulations on (in­
finitary) propositional derivations. These operational aspects are described in­


Source: Aehlig, Klaus T. - Institut für Informatik, Ludwig-Maximilians-Universität München


Collections: Mathematics; Computer Technologies and Information Sciences