# On reduction between two classes?

https://link.springer.com/article/10.1007/s00153-013-0351-x gives seven reductions $m,c,d,p,btt(1),\ell,tt$.

1. What does norm $1$ mean in $btt(1)$?

2. Is there illustrative examples that help understand from hierarchy between $PP$ and $PSPACE$ the different reductions?

3. Which is the standard reduction existence or non-existence that we care when we prove class inclusions or should prove to separate classes?