# What are some problems in EXP not known to be EXPTIME-Complete, but also do not have any known algorithm in NP?

These would be problems known to be in exp where there could hypothetically be a P or NP algorithm, but none have been discovered yet if one is possible.

• The title doesn't match the body. "not known to be in NP" is different from "there could hypothetically be a polynomial time algorithm, but none have been discovered yet if one is possible". Please put the question in the body of the post. The title should be a short summary.
– D.W.
Jan 7 at 22:07
• @ D.W.♦ I fixed it. Jan 7 at 22:13
• cstheory.stackexchange.com/q/799/5038
– D.W.
Jan 7 at 22:44

Assuming that $$NP\not= PSPACE$$ and $$PSPACE \not= EXPTIME$$, all $$PSPACE$$-complete problems are incomplete in $$EXPTIME$$