In computational complexity theory, the complexity class 2-EXPTIME (sometimes called 2-EXP) is the set of all decision problems solvable by a deterministic Turing machine in O(22p(n)) time, where p(n) is a polynomial function of n. In terms of DTIME, We know 2-EXPTIME can also be reformulated as the space class AEXPSPACE, the problems that can be solved by an alternating Turing machine in exponential space.
The class 3-EXPTIME is defined similarly to 2-EXPTIME but with a triply exponential time bound
Examples of algorithms that require at least 2-EXPTIME include: Generalizations of many fully observable games are EXPTIME-complete.
These games can be viewed as particular instances of a class of transition systems defined in terms of a set of state variables and actions/events that change the values of the state variables, together with the question of whether a winning strategy exists.
A generalization of this class of fully observable problems to partially observable problems lifts the complexity from EXPTIME-complete to 2-EXPTIME-complete.