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Journal of Logic and Computation Advance Access originally published online on September 5, 2008
Journal of Logic and Computation 2009 19(2):323-339; doi:10.1093/logcom/exn054
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Proof Complexity of the Cut-free Calculus of Structures

Emil Jerábek

Institute of Mathematics of the Academy of Sciences, Zitná 25, 115 67 Praha 1, Czech Republic.

E-mail: jerabek{at}math.cas.cz

Received 26 November 2007.


  Abstract

We investigate the proof complexity of analytic subsystems of the deep inference proof system SKSg (the calculus of structures). Exploiting the fact that the cut rule (i{uparrow}) of SKSg corresponds to the ¬-left rule in the sequent calculus, we establish that the ‘analytic'system KSg+c{uparrow} has essentially the same complexity as the monotone Gentzen calculus MLK. In particular, KSg+c{uparrow} quasipolynomially simulates SKSg, and admits polynomial-size proofs of some variants of the pigeonhole principle.

Keywords: proof complexity; calculus of structures; monotone sequent calculus; cut rule


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