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Does there exist a language which is PSPACE-complete and regular? (reduction is polynomial with regard to time).

Correct answer here is "unknown". I can't prove it. Can you help me?

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There exists a PSPACE-complete regular language if and only if P=PSPACE, which is unknown.

In fact, we can say even more: the language $\{1\}$ is PSPACE-complete if and only if P=PSPACE.

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  • $\begingroup$ Is it about that each regular language is in $P$ ? $\endgroup$ – Haskell Fun Aug 27 '17 at 9:16
  • $\begingroup$ This is definitely part of the matter. $\endgroup$ – Yuval Filmus Aug 27 '17 at 9:46

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