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Comparing the Complexity of Cut-Elimination Methods

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Proof Theory in Computer Science (PTCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2183))

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Abstract

We investigate the relative complexity of two different methods of cut-elimination in classical first-order logic, namely the methods of Gentzen and Tait. We show that the methods are incomparable, in the sense that both can give a nonelementary speed-up of the other one. More precisely we construct two different sequences of LK-proofs with cuts where cut-elimination for one method is elementary and nonelementary for the other one. Moreover we show that there is also a nonelementary difference in complexity for different deterministic versions of Gentzen’s method.

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References

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Authors and Affiliations

  1. Institut für Computermathematik (E-118), TU-Vienna, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria

    Matthias Baaz

  2. Institut für Computersprachen (E-185), TU-Vienna, Favoritenstraße 9, 1040, Vienna, Austria

    Alexander Leitsch

Authors
  1. Matthias Baaz
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  2. Alexander Leitsch
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Editor information

Editors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, 72076, Tübingen, Germany

    Reinhard Kahle  & Peter Schroeder-Heister  & 

  2. Theoretische Informatik, ETH Zürich, ETH Zentrum, 8092, Zürich, Switzerland

    Robert Stärk

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© 2001 Springer-Verlag Berlin Heidelberg

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Baaz, M., Leitsch, A. (2001). Comparing the Complexity of Cut-Elimination Methods. In: Kahle, R., Schroeder-Heister, P., Stärk, R. (eds) Proof Theory in Computer Science. PTCS 2001. Lecture Notes in Computer Science, vol 2183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45504-3_4

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  • DOI: https://doi.org/10.1007/3-540-45504-3_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42752-0

  • Online ISBN: 978-3-540-45504-2

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