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Journal of Logic and Computation Advance Access originally published online on May 30, 2007
Journal of Logic and Computation 2007 17(3):587-604; doi:10.1093/logcom/exm017
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

On Independence of Variants of the Weak Pigeonhole Principle

Emil Jerábek

Institute of Mathematics, AS CR, Zitná 25, 115 67 Praha 1, Czech Republic. E-mail: jerabek@math.cas.cz

Received 14 August 2006.


  Abstract

The principle Formula states that no oracle circuit can compute a surjection of a onto b. We show that Formula is independent of Formula for various choices of the parameters {pi}, {Pi}, {varrho}, P. We also improve the known separation of iWPHP(PV) from Formula under cryptographic assumptions.

Keywords: Bounded arithmetic; pigeonhole principle; KPT witnessing; Boolean circuit


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