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On the computational complexity of cutreduction
 

Summary: On the computational complexity of
cut­reduction
Klaus Aehlig Arnold Beckmann
Department of Computer Science
University of Wales Swansea
Singleton Park, Swansea SA2 8PP, UK
{k.t.aehlig|a.beckmann}@swansea.ac.uk
February 15, 2009
Abstract
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