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Revision #1 to TR02-023 | 3rd September 2002 00:00

Bounded-depth Frege lower bounds for weaker pigeonhole principles

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Revision #1
Authors: Joshua Buresh-Oppenheim, Paul Beame, Ran Raz, Ashish Sabharwal
Accepted on: 3rd September 2002 00:00
Downloads: 1188
Keywords: 


Abstract:


Paper:

TR02-023 | 16th April 2002 00:00

Bounded-depth Frege lower bounds for weaker pigeonhole principles





TR02-023
Authors: Josh Buresh-Oppenheim, Paul Beame, Ran Raz, Ashish Sabharwal
Publication: 17th April 2002 19:15
Downloads: 1126
Keywords: 


Abstract:

We prove a quasi-polynomial lower bound on the size of bounded-depth
Frege proofs of the pigeonhole principle $PHP^{m}_n$ where
$m= (1+1/{\polylog n})n$.
This lower bound qualitatively matches the known quasi-polynomial-size
bounded-depth Frege proofs for these principles.
Our technique, which uses a switching lemma argument like other lower bounds
for bounded-depth Frege proofs, is novel in that the tautology to which
this switching lemma is applied remains random throughout the argument.



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