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...g strategy in the game represented by <math>\Phi</math>. FORMULA-GAME is [[PSPACE-complete]] because it is exactly the same decision problem as [[True quantified Bool [[Category:Satisfiability problems]] ...

{{Short description|Set of decision problems}} If we denote by SPACE(''f''(''n'')), the set of all problems that can be solved by [[Turing machines]] using ''O''(''f''(''n'')) space f ...

...izations of games are needed, as games on a fixed size of board are finite problems. ...SPACE-complete]]. Generalized [[hex (board game)|hex]] and [[reversi]] are PSPACE-complete.<ref>{{citation ...

...be thought of as the hardest problems in [[PSPACE]], the class of decision problems solvable in polynomial space, because a solution to any one such problem co ...as]], step-by-step changes between solutions of combinatorial optimization problems, and many puzzles and games. ...

EXPTIME can also be reformulated as the space class APSPACE, the set of all problems that can be solved by an [[alternating Turing machine]] in polynomial space ...versus NP problem|P = NP]], then EXPTIME {{=}} [[NEXPTIME]], the class of problems solvable in exponential time by a [[nondeterministic Turing machine]].<ref> ...

...h-table reduction]] from a problem ''A'' to a problem ''B'' (both decision problems) is a polynomial time algorithm for transforming inputs to problem ''A'' in ...to define complete problems for other complexity classes, including the [[PSPACE-complete|'''PSPACE'''-complete]] [[Formal language|languages]] and [[EXPTIME|'''EXPT ...

...(complexity)|P]], [[NP (complexity)|NP]], NP-complete, and NP-hard set of problems. The left side is valid under the assumption that [[P versus NP problem|P≠N ...NP|P≠NP]], it is unlikely that any polynomial-time algorithms for NP-hard problems exist.<ref>{{cite book |author1=Daniel Pierre Bovet |title=Introduction to ...

"The hardest problems" of a class refer to problems which belong to the class such that every other problem of that class can b |[[Sharp-P-complete|#P-complete]]||The hardest problems in #P ...

...ational complexity theory]], '''generalized geography''' is a well-known [[PSPACE-complete]] problem. ...g which player has a winning strategy in a generalized geography game is [[PSPACE-complete]]. ...

That is, '''co-NP''' is the set of decision problems where there exists a polynomial {{tmath|p(n)}} and a polynomial-time bounde ==Complementary problems== ...

...zons played on a n x n grid, started from an arbitrary configuration) is [[PSPACE-complete]].<ref>{{citation | contribution = Generalized Amazons is PSPACE-complete ...

...ty |eprint=cs/0502068|year=2005}}</ref> showed that ''Rush Hour'' is still PSPACE-complete when the cars are of size 2 only. They also conjectured that ''Rush Hour'' [[Category:PSPACE-complete problems]] ...

Classes within the hierarchy have complete problems (with respect to [[polynomial-time reduction]]s) that ask if [[quantified B ..., and <math> \Delta_2^\mathrm{P} = \mathrm{P^{NP}} </math> is the class of problems solvable in polynomial time by a deterministic Turing machine with an oracl ...

{{Short description|Set of decision problems}} ...Sans-serif|EXPSPACE-complete}} problems might be thought of as the hardest problems in {{Sans-serif|EXPSPACE}}. ...

{{short description|Class of problems solvable in polynomial time}} ..." or "[[tractable problem|tractable]]". This is inexact: in practice, some problems not known to be in P have practical solutions, and some that are in P do no ...

...cally checkable proof]]s. Recall that '''NP''' can be seen as the class of problems where an all-powerful prover gives a purported proof that a string is in th ...at NEXPTIME-complete problems are not in NP; it has been proven that these problems cannot be verified in [[polynomial time]], by the [[time hierarchy theorem] ...

== Decision problems == CTL* model checking (of an input formula on a fixed model) is PSPACE-complete <ref name=":0">{{Cite book|url=http://dl.acm.org/citation.cfm?id=1373322|ti ...

...uppose that only a polynomial number of processors are required for some [[PSPACE-complete|'''PSPACE'''-complete]] problem, then it would show that '''PSPACE''' = ''' ...lems are the same for all computers, but also that the feasibly computable problems are the same for all computers. ...

The mathematical structure generated on a set of problems by the reductions of a particular type generally forms a [[preorder]], whos ...ly two numbers, we can square a number. This seems to imply that these two problems are equally hard. This kind of reduction corresponds to [[Turing reduction] ...

...t of an insertion sort is optimum, i.e., a correctly sorted list. For many problems, online algorithms cannot match the performance of offline algorithms. If t ...c algorithm]]: focusing on the time complexity of maintaining solutions to problems with online inputs. ...