A Quasipolynomial Cut-Elimination Procedure in Deep Inference via Atomic Flows and Threshold Formulae

  • Paola Bruscoli
  • Alessio Guglielmi
  • Tom Gundersen
  • Michel Parigot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6355)

Abstract

Jeřábek showed in 2008 that cuts in propositional-logic deep-inference proofs can be eliminated in quasipolynomial time. The proof is an indirect one relying on a result of Atserias, Galesi and Pudlák about monotone sequent calculus and a correspondence between this system and cut-free deep-inference proofs. In this paper we give a direct proof of Jeřábek’s result: we give a quasipolynomial-time cut-elimination procedure in propositional-logic deep inference. The main new ingredient is the use of a computational trace of deep-inference proofs called atomic flows, which are both very simple (they trace only structural rules and forget logical rules) and strong enough to faithfully represent the cut-elimination procedure.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Paola Bruscoli
    • 1
    • 2
  • Alessio Guglielmi
    • 1
    • 2
  • Tom Gundersen
    • 1
    • 2
  • Michel Parigot
    • 3
  1. 1.University of BathUK
  2. 2.LORIA & INRIA Nancy-Grand EstFrance
  3. 3.Laboratoire PPSUMR 7126, CNRS & Université Paris 7France

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