On Independence of Variants of the Weak Pigeonhole Principle

The principle sPHPa b (PV (α)) states that no oracle circuit can compute a surjection of a onto b. We show that sPHP (a) P (a)(PV (α)) is independent of PV1(α)+sPHP π(a) Π(a)(PV (α)) for various choices of the parameters π, Π, , P. We also improve the known separation of iWPHP(PV ) from S1 2 + sWPHP(PV ) under cryptographic assumptions.

• Type: Journal
• Year: 2007
• Where: LOGCOM
• Authors: Emil Jerábek
• Keywords: LOGCOM 2007, Oracle Circuit, Principle SPHPa, Various Choices