Editing PSPACE-complete (section)

===Formal languages===
Given a [[regular expression]] <math>R</math>, determining whether it generates every string over its alphabet is PSPACE-complete.{{r|hunt}}

The first known PSPACE-complete problem was the [[word problem (computability)|word problem]] for [[deterministic computation|deterministic]] [[context-sensitive grammar]]s. In the word problem for context-sensitive grammars, one is given a set of grammatical transformations which can increase, but cannot decrease, the length of a sentence, and wishes to determine if a given sentence could be produced by these transformations. The technical condition of "determinism" (implying roughly that each transformation makes it obvious that it was used) ensures that this process can be solved in polynomial space, and {{harvtxt|Kuroda|1964}} showed that every (possibly non-deterministic) program computable in [[linear space]] could be converted into the parsing of a context-sensitive grammar, in a way which preserves determinism.{{r|kuroda}} In 1970, [[Savitch's theorem]] showed that PSPACE is closed under nondeterminism, implying that even non-deterministic context-sensitive grammars are in PSPACE.{{r|garey-johnson}}