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PSPACE

In complexity theory the class PSPACE is the set of decision problems that can be solved by a Turing machine using a polynomial amount of memory, and unlimited time.

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):

NC <= P <= NP <= PSPACE

NC < PSPACE < EXPSPACE

PSPACE-Complete <= PSPACE

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.



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