Formally PSPACE is defined as the class of formal languages that are recognizable in polynomial space. Defining P and NP as the classes of languages recognizable in polynomial time and recognizable in polynomial time on a nondeterministic Turing machine, respectively (see P=NP question), it can be shown that P is a subset of PSPACE and that NP is also a subset of PSPACE. It is not known, however, whether NP = PSPACE
although it is conjectured that they are different, i.e. that there exist languages in PSPACE that are not in NP.
Many problems associated with recognizing whether a player of a certain game (like GO) has a forced win from a given position are PSPACE-complete, which is defined in a similar manner to NP-completeness (see P=NP question). This implies that such languages can be recognized in polynomial time only if PSPACE = P
Such problems can thus be considered to be even harder than NP-complete problems.
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