Space-bounded hierarchies and probabilistic computations

• Authors: Walter L. Ruzzo;Janos Simon;Martin Tompa
• Venue: STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
• Year: 1982

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].