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Set of decision problems From Wikipedia, the free encyclopedia
In computational complexity theory, EXPSPACE 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 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.
In terms of DSPACE and NSPACE,
An example of an EXPSPACE-complete 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 (zero or more copies of an expression), and squaring (two copies of an expression).[1]
Alur and Henzinger extended linear temporal logic with times (integer) and prove that the validity problem of their logic is EXPSPACE-complete.[2]
The coverability problem for Petri Nets is EXPSPACE-complete.[3]
The reachability problem for Petri nets was known to be EXPSPACE-hard for a long time,[4] but shown to be nonelementary,[5] so probably not in EXPSPACE. In 2022 it was shown to be Ackermann-complete.[6][7]
EXPSPACE is known to be a strict superset of PSPACE, NP, and P. It is further suspected to be a strict superset of EXPTIME, however this is not known.