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 "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 **PSPACE**-Complete problems. See **PSPACE**-Complete for examples of problems that are suspected to be in **PSPACE** but not in **NP**.