We introduce a new nondeterministic oracle model. Our model is significantly different from all previous space-bounded oracle models, and has the following properties: First, it permits a nontrivial NL-hierarchy, which does not collapse without a similar consequence for the polynomial-time hierarchy. This is immediate from the result that k p is exactly the 2kth level in our NL-hierarchy, for all k1. On the other hand, it still behaves very well in relativised worlds. In particular, the new model satisfies the Immerman-Szelepcsenyi theorem and Savitch's theorem in the relativized worlds for oracle sets in each level of the polynomial-time hierarchy. 1991.
