# Ruzzo-Simon-Tompa oracle access mechanism

In a paper on relativizing logspace computations, Ladner and Lynch construct an oracle relative to which $\mathsf{NL} \nsubseteq \mathsf{P}$. There are some more pathological examples in this vein in the literature. I have been reading some papers on relativized small space classes, and one of the primary tools in this area is the Ruzzo-Simon-Tompa(RST) oracle access mechanism which demands that a non-deterministic space-bounded turing machine act deterministically while making queries to the oracle.

Now consider circuit families with oracle gates - say, $A^B$, where $A$ is a circuit complexity class containing logspace with oracle access to another class $B$, via oracle gates appended to the basis of $A$. Are there any pathological examples similar in spirit to the Ladner-Lynch paper, known for such classes? What would be a RST-like restriction necessary for such classes? In case there are indeed such examples, am I right in guessing that a RST analogue would be to insist that $A$ be a logspace-uniform circuit family?

A definition of oracle access that works for small circuit complexity classes (the $AC^k$ and $NC^k$ hierarchies) as well as for logarithmic space classes, with the property that all known inclusions relativize, can be found in this paper: