Adaptive logspace and depth-bounded reducibilities

Abstract

We discuss a number of results regarding an important subject: the study of the computational power of depth-bounded reducibilities, their use to classify the complexity of computational problems, and their characterizations in terms of other computational models. In particular, problems arising in the design of concurrent systems are studied, and two kinds of logarithmic space reductions are defined. The first one is nonadaptive and equivalent in many respects to the oracle set model. The second one provides a notion of adaptive logspace reducibility which turns out to characterize precisely depth-bounded reductions. The closures of NP under these reducibilities are also treated. This is a conference delivered at Structure in Complexity Theory 6th Annual Conference, Chicago 1991, and appears in the proceedings in the present form.