The exact complexity of the weak pigeonhole principle is an old and fundamental problem in proof complexity. Using a diagonalization argument, Paris, Wilkieand Woods 16] showed ho...
We study the extension (introduced as BT in [5]) of the theory S1 2 by instances of the dual (onto) weak pigeonhole principle for p-time functions, dWPHP(PV )x x2 . We propose a n...
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)...