space-bounded TMs and oracles In general, the query-tape for an oracle counts towards the space-complexity of a TM. However, it seems plausible to allow a write-only oracle-tape (such as is used in L-space reductions).

Is such a construction useful? Does it yield any particularly absurd results?
I think one surprising fact is that in this model Savitch's theorem doesn't "obviously" relativize. That is, one can see that $PSPACE^P=EXPTIME$ and $NPSPACE^P=NEXPTIME$ in this model, and we don't currently know that $EXPTIME=NEXPTIME$ (and Savitch's theorem in this context does not seem to give it).  I'd be interested in whether this can be pushed to "provably" non-relativizing.

One can also observe that $NL^{NL}=NL^L=NP$ in this model.

However, I think that this model is at least worth thinking about, with respect to issues of relativization in the space hierarchy theorem.  Also, in some sense, I want $L^A$ to make poly-sized queries to $A$.