Adaptive logspace and depth-bounded reducibilities

The author discusses a number of results regarding 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 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