Abstract
An important open problem relating sequential and parallel computations is whether the space complexity on Turing machines is linearly related to the depth complexity on uniform circuits. Some graph problems have been successfully proved to be complete for DSPACE(log n) under (log n)-depth Turing reducibility [3]. In this paper, we discuss (log n)-depth many-one reducibility which is proved to be weaker than (log n)-depth Turing reducibility. A new complete language for DSPACE(log n) under our reducibility is presented.
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