EXPSPACE

In computational complexity theory, EXPSPACE is the set of all decision problems solvable by a deterministic Turing machine in exponential space, i.e., in ${\displaystyle O(2^{p(n)})}$ space, where ${\displaystyle p(n)}$ is a polynomial function of ${\displaystyle n}$. Some authors restrict ${\displaystyle p(n)}$ to be a linear function, but most authors instead call the resulting class ESPACE. If we use a nondeterministic machine instead, we get the class NEXPSPACE, which is equal to EXPSPACE by Savitch's theorem.

A decision problem is EXPSPACE-complete if it is in EXPSPACE, and every problem in EXPSPACE has a polynomial-time many-one reduction to it. In other words, there is a polynomial-time algorithm that transforms instances of one to instances of the other with the same answer. EXPSPACE-complete problems might be thought of as the hardest problems in EXPSPACE.

EXPSPACE is a strict superset of PSPACE, NP, and P and is believed to be a strict superset of EXPTIME.