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On the Computational Complexity of Cut-Reduction Klaus Aehlig Arnold Beckmann
 

Summary: On the Computational Complexity of Cut-Reduction
Klaus Aehlig Arnold Beckmann
Department of Computer Science
Swansea University
Singleton Park, Swansea SA2 8PP, UK
E-mail: {k.t.aehlig|a.beckmann}@swansea.ac.uk
Abstract
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.
1 Introduction
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

  

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

 

Collections: Mathematics; Computer Technologies and Information Sciences