The definition is not affected by whether the Turing machine is deterministic or nondeterministic. So PSPACE=NPSPACE. The set PSPACE is a strict superset of the set of contextsensitive languages. The following facts are known, where "<" means "strict subset", and "<=" means "subset" (unknown whether they are equal):
There are three <= symbols on the first line. It is known that at least one of them is a <, but it is not known which. It is widely suspected that all three are <. A proof of that for the middle one is worth $1,000,000. It is also widely suspected that the <= on the last line should be a <.
The hardest problems in PSPACE are the PSPACEComplete problems. See PSPACEComplete for examples of problems that are suspected to be in PSPACE but not in NP.
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