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Space bounded computations: Review and new separation results. (English) Zbl 0745.68051

Summary: We review the key results about space bounded complexity classes, discuss the central open problems and outline the prominent proof techniques. We show that, for a slightly modified Turing machine model, low level deterministic and nondeterministic space bounded complexity classes are different. Furthermore, for this computation model, we show that Savitch’s theorem and the Immerman-Szelepcsényi theorem do not hold in the range \(\lg \lg n\) to \(\lg n\). We also present other changes in the computation model which bring out and clarify the importance of space constructibility. We conclude by enumerating open problems which arise out of the discussion.

MSC:

68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
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