Double exponential problems?

Question

Are there any significant problems in computer science that can only be solved in double exponential time ? And if they exist then to which class of problems do they belong ?

Answer 1

From Wikipedia:

In computational complexity theory, some algorithms take double-exponential time:

• Each decision procedure for Presburger arithmetic provably requires at least double-exponential time

• Computing a Gröbner basis over a field. In the worst case, a Gröbner basis may have a number of elements which is doubly exponential in the number of variables.

• Finding a complete set of associative-commutative unifiers

• Satisfying CTL+ (which is, in fact, 2-EXPTIME-complete)

• Quantifier elimination on real closed fields takes a doubly-exponential time (see Cylindrical algebraic decomposition).

• Calculating the complement of a regular expression