EXPSPACE
In computational complexity theory, is the set of all decision problems solvable by a deterministic Turing machine in exponential space, i.e., in space, where is a polynomial function of. Some authors restrict to be a linear function, but most authors instead call the resulting class. If we use a nondeterministic machine instead, we get the class, which is equal to by Savitch's theorem.
A decision problem is if it is in, and every problem in 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. problems might be thought of as the hardest problems in.
is a strict superset of,, and. It contains and is believed to strictly contain it, but this is unproven.
Formal definition
In terms of and,Examples of problems
Formal languages
An example of an problem is the problem of recognizing whether two regular expressions represent different languages, where the expressions are limited to four operators: union, concatenation, the Kleene star, and squaring.Logic
Alur and Henzinger extended linear temporal logic with times and prove that the validity problem of their logic is EXPSPACE-complete.Reasoning in the first-order theory of the real numbers with +, ×, = is in EXPSPACE and was conjectured to be EXPSPACE-complete in 1986.
Petri nets
The coverability problem for Petri Nets is -complete.The reachability problem for Petri nets was known to be -hard for a long time, but shown to be nonelementary, so probably not in. In 2022 it was shown to be Ackermann-complete.