Possibility of hierarchy with $UP$ class? I am not sure if this is a cheap query. However I am unable to find this myself. So I am posting here. The standard complexity class is built with $NP$ and $coNP$ and leads up to $PSPACE$. The reference https://link.springer.com/content/pdf/10.1007%2FBF01184809.pdf gives some classes for which we have oracles with respect to which $UP$ is not low.


Which classes are known to be low with $UP$ oracle ($PSPACE$ is one of them)?
Is there a hierarchy to concoct with $UP$ and $coUP$ analogous to the standard polynomial hierarchy and in particular is there an analog of $PSPACE$?
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.