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All reports by Author Alan Woods:

TR94-018 | 12th December 1994
Jan Krajicek, Pavel Pudlak, Alan Woods

An Exponential Lower Bound to the Size of Bounded Depth Frege Proofs of the Pigeonhole Principle

We prove lower bounds of the form $exp\left(n^{\epsilon_d}\right),$
$\epsilon_d>0,$ on the length of proofs of an explicit sequence of
tautologies, based on the Pigeonhole Principle, in proof systems
using formulas of depth $d,$ for any constant $d.$ This is the
largest lower bound for the strongest proof system, for which ... more >>>

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