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Sharpened lower bounds for cut elimination

Published online by Cambridge University Press:  12 March 2014

Samuel R. Buss
Samuel R. Buss*
Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla, Ca 92093-0112, USA, E-mail: [email protected]
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Abstract

We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our results remove the constant of proportionality, giving an exponential stack of height equal to d − O(1). The proof method is based on more efficiently expressing the Gentzen–Solovay cut formulas as low depth formulas.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 656 - 668
Copyright
Copyright © Association for Symbolic Logic 2012

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