complements of all problems in PSPACE are also in PSPACE, meaning that co-PSPACE = PSPACE. The following relations are known between PSPACE and the complexity classes...

In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input...

also known to be no larger than PSPACE, the class of problems decidable in polynomial space. Again, whether P = PSPACE is an open problem. To summarize:...

need not store game states; however many games of interest are known to be PSPACE-hard, and it follows that their space complexity will be lower-bounded by...

hypothetical technologies List of NP-complete problems List of paradoxes List of PSPACE-complete problems List of undecidable problems List of unsolved deaths Lists...

the classes NP and co-NP. Each class in the hierarchy is contained within PSPACE. The hierarchy can be defined using oracle machines or alternating Turing...

problems solvable by an interactive proof system. It is equal to the class PSPACE. The result was established in a series of papers: the first by Lund, Karloff...

Second-order logic with a transitive closure (commutative or not) yields PSPACE, the problems solvable in polynomial space. Second-order logic with a least...

For instance P ⊆ NP ⊆ PP ⊆ PSPACE, but it is possible that P = PSPACE. If P is not equal to NP, then P is not equal to PSPACE either. Since there are many...

is in EXPSPACE, and is PSPACE-hard. It's proved to be PSPACE-hard by reducing Generalized Geography, a problem known to be PSPACE-hard, to a game of Ghost...

complexity classes relate to each other in the following way: L⊆NL⊆P⊆NP⊆PSPACE⊆EXPTIME⊆NEXPTIME⊆EXPSPACE (where ⊆ denotes the subset relation). However...

\exists z\ ((x\lor z)\land y)} QBF is the canonical complete problem for PSPACE, the class of problems solvable by a deterministic or nondeterministic Turing...

Here are some of the more commonly known problems that are PSPACE-complete when expressed as decision problems. This list is in no way comprehensive. Generalized...

complexity. Without ko, Go is PSPACE-hard. This is proved by reducing True Quantified Boolean Formula, which is known to be PSPACE-complete, to generalized...

polynomial space, but not in non-deterministic polynomial time (unless NP = PSPACE). NP-hard problems do not have to be elements of the complexity class NP...

⁠ is symmetrical. co-NP is a subset of PH, which itself is a subset of PSPACE. An example of a problem that is known to belong to both NP and co-NP (but...

computational complexity theory, generalized geography is a well-known PSPACE-complete problem. Geography is a children's game, where players take turns...

to identify musical notes without a reference tone AP (complexity), or PSPACE, problems decidable by a Turing machine Wireless access point, for WiFi...

are strict subsets, since we don't even know if P is a strict subset of PSPACE. BPP is contained in the second level of the polynomial hierarchy and therefore...

PP\subseteq PSPACE\subseteq EXP}}} As the problem of ⁠ P   = ?   P S P A C E {\displaystyle {\mathsf {P}}\ {\stackrel {?}{=}}\ {\mathsf {PSPACE}}} ⁠ has...

basic time and space complexity classes in the following way: P ⊆ NP ⊆ PSPACE ⊆ EXPTIME ⊆ NEXPTIME ⊆ EXPSPACE. Furthermore, by the time hierarchy theorem...

use O ( f ( n ) ) {\displaystyle O(f(n))} space. The complexity classes PSPACE and NPSPACE allow f {\displaystyle f} to be any polynomial, analogously...

NC = P problem NP = co-NP problem P = BPP problem P = PSPACE problem L = NL problem PH = PSPACE problem L = P problem L = RL problem Unique games conjecture...

prove that IP = PSPACE. However, in 2008, Scott Aaronson and Avi Wigderson showed that the main technical tool used in the IP = PSPACE proof, known as...

exponential time, a very large class. NEXPTIME contains PSPACE, and is believed to strictly contain PSPACE. Adding a constant number of additional provers beyond...

removing all tiles is PSPACE-complete, and the game is NP-complete if looking below tiles is allowed. It has been proven that it is PSPACE-hard to approximate...

the drawing rule in standard Checkers), then the problem is in PSPACE, thus it is PSPACE-complete. However, without this bound, Checkers is EXPTIME-complete...

computational problem that is known to be NP-hard and in PSPACE, but is not known to be complete for NP, PSPACE, or any language in the polynomial hierarchy. ∃...

are uniform (generated by a polynomial-time algorithm). PP is included in PSPACE. This can be easily shown by exhibiting a polynomial-space algorithm for...

}{=}}{\mathsf {PSPACE}}} ⁠ (more unsolved problems in computer science) PH contains almost all well-known complexity classes inside PSPACE; in particular...