Possibility of hierarchy with $UP$ class?
Problem 2. answered in references

a. https://arxiv.org/pdf/cs/9907033.pdf

b. http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=19DD617ABDB31709CA0BEF797C283867?doi=10.1.1.60.9357&amp;rep=rep1&amp;type=pdf.