Abstract
This paper studies two aspects of the power of space-bounded probabilistic Turing machines. Section 2 presents a simple alternative proof of Simon's recent result [13] that space-bounded probabilistic complexity classes are closed under complement. Section 3 demonstrates that any language in the log n space hierarchy can be recognized by an log n space-bounded probabilistic Turing machine with small error; this is a generalization of Gill's result that any language in NSPACE(log n) can be recognized by such a machine The second result raises interesting questions about space hierarchies, which are considered in section 4. The usual definition is in terms of space-bounded alternating Turing machines with a constant number of alternations [4].
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