Some Quick Ideas

Sashka’s Technique applied to pFBP The key step in Sashka and Russel’s technique to prove lower bounds for pFBT was to prove that for each path p of length l, PrI [S(I) ⊢ PSp | I ⊢ PIp] ≤ 1 f . We extend this to a technique for pFBP. The key step is to prove that for each node v at depth l, PrI [S(I) ⊢ PSv | I ⊢ PIv] ≤ 1 f . My intuition was that PrI [S(I) ⊢ PSv | I ⊢ PIv] ≤ maxp∈v PrI [S(I) ⊢ PSp | I ⊢ PIp]. However, in general this is not true. See Section 2