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The definition is not affected by whether the Turing machine is deterministic or non-deterministic. So PSPACE=NPSPACE. The set PSPACE is a strict superset of the set of context-sensitive languages. The following facts are known, where means "proper 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 PSPACE-Complete problems. See PSPACE-Complete for examples of problems that are suspected to be in PSPACE but not in NP.