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Algorithmic complexity class
In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that are solvable
EXPTIME
Set of problems in computational complexity theory
complexity classes relate to each other in the following way: L⊆NL⊆P⊆NP⊆PSPACE⊆EXPTIME⊆NEXPTIME⊆EXPSPACE Where ⊆ denotes the subset relation. However, many relationships
Complexity_class
Complexity class
In computational complexity theory, the complexity class 2-EXPTIME (sometimes called 2-EXP, sometimes also written 2EXPTIME) is the set of all decision
2-EXPTIME
Estimate of time taken for running an algorithm
belong to the complexity class 2-EXPTIME. 2-EXPTIME = ⋃ c ∈ N DTIME ( 2 2 n c ) {\displaystyle {\textsf {2-EXPTIME}}=\bigcup _{c\in \mathbb {N} }{\textsf
Time_complexity
Unsolved problem in computer science
polynomial function of n. A decision problem is EXPTIME-complete if it is in EXPTIME, and every problem in EXPTIME has a polynomial-time many-one reduction to
P_versus_NP_problem
Inherent difficulty of computational problems
instance, the time hierarchy theorem tells us that P is strictly contained in EXPTIME, and the space hierarchy theorem tells us that L is strictly contained
Computational complexity theory
Computational_complexity_theory
Game generalized so that it can be played on a board or grid of any size
player in a given position is EXPTIME-complete. Generalized chess, go (with Japanese ko rules), Quixo, and checkers are EXPTIME-complete. Game complexity
Generalized_game
Class of computational complexity
PSPACE}}\\{\mathsf {PSPACE\subseteq EXPTIME\subseteq EXPSPACE}}\\{\mathsf {NL\subset PSPACE\subset EXPSPACE}}\\{\mathsf {P\subset EXPTIME}}\end{array}}} From the
PSPACE
Calculations of the game complexity of Go
rule. Though Go with Japanese ko rule is EXPTIME-complete, both the lower and the upper bounds of Robson’s EXPTIME-completeness proof break when the superko
Go_and_mathematics
Generalization of a Markov decision process
EXPTIME-complete EXPTIME-complete undecidable EXPTIME-complete undecidable undecidable coBüchi undecidable EXPTIME-complete EXPTIME-complete EXPTIME-complete
Partially observable Markov decision process
Partially_observable_Markov_decision_process
Notion in combinatorial game theory
original (PDF) on 2016-04-03. J. M. Robson (1984). "N by N checkers is Exptime complete". SIAM Journal on Computing. 13 (2): 252–267. doi:10.1137/0213018
Game_complexity
Class of problems solvable in polynomial time
{NP}}\subseteq {\mathsf {PSPACE}}={\mathsf {NPSPACE}}\subseteq {\mathsf {EXPTIME}}.} Here, EXPTIME is the class of problems solvable in exponential time. Of all
P_(complexity)
Strategy board game
thus it is PSPACE-complete. However, without this bound, Checkers is EXPTIME-complete. However, other problems have only polynomial complexity: Can
Checkers
Complexity class used to classify decision problems
not have to consider proofs longer than this). NP is also contained in EXPTIME, since the same algorithm operates in exponential time. co-NP contains
NP_(complexity)
Exponential function of an exponential function
and is a superset of EXPSPACE. An example of a problem in 2-EXPTIME that is not in EXPTIME is the problem of proving or disproving statements in Presburger
Double_exponential_function
Topics referred to by the same term
compounds like food or medicines Experience points, in role-playing games EXPTIME, a complexity class in computing Ford EXP, a car manufactured in the 1980s
Exp
Concept in computational complexity theory
We know P ⊆ NP ⊆ EXPTIME ⊆ NEXPTIME and also, by the time hierarchy theorem, that NP ⊊ NEXPTIME If P = NP, then NEXPTIME = EXPTIME (padding argument);
NEXPTIME
Computational complexity class
equal to the complexity class DTIME(2O(n)). E, unlike the similar class EXPTIME, is not closed under polynomial-time many-one reductions. E is contained
E_(complexity)
Set of decision problems
EXPSPACE. EXPSPACE is a strict superset of PSPACE, NP, and P. It contains EXPTIME and is believed to strictly contain it, but this is unproven. In terms
EXPSPACE
Impossible task in computing
allowing ± p , ± q {\displaystyle \pm p,\pm q} , but this extension is EXPTIME-complete (Theorem 2.24). The first-order logic fragment where the only
Entscheidungsproblem
Branch of artificial intelligence
showed in 1998 that with branching actions, the planning problem becomes EXPTIME-complete. A particular case of contiguous planning is represented by FOND
Automated planning and scheduling
Automated_planning_and_scheduling
Growth of quantities at rate proportional to the current amount
growth Cell growth Combinatorial explosion Exponential algorithm EXPSPACE EXPTIME Hausdorff dimension Hyperbolic growth Information explosion Law of accelerating
Exponential_growth
Given more time, a Turing machine can solve more problems
⊊ EXPTIME ⊊ 2-EXP ⊊ ... and NP ⊊ NEXPTIME ⊊ 2-NEXP ⊊ .... For example, P ⊊ E X P T I M E {\displaystyle {\mathsf {P}}\subsetneq {\mathsf {EXPTIME}}}
Time_hierarchy_theorem
Concept in computer science
exists an oracle relative to which ZPP = EXPTIME. A proof for ZPP = EXPTIME would imply that P ≠ ZPP, as P ≠ EXPTIME (see time hierarchy theorem). BPP RP
ZPP_(complexity)
many complexity classes, including the hierarchy of time classes P, EXPTIME, 2-EXPTIME,… and the space classes L, PSPACE, EXPSPACE,…; as well as the classes
Implicit computational complexity
Implicit_computational_complexity
Deterministic time, in computational complexity theory
"computationally feasible". A much larger class using deterministic time is EXPTIME, which contains all of the problems solvable using a deterministic machine
DTIME
Board game
problem of determining if the first player has a win in a given position is EXPTIME-complete. The July 2007 announcement by Chinook's team stating that the
English_draughts
Japanese strategy board game
two. From a computational complexity point of view, generalized shogi is EXPTIME-complete. Hundreds of video games were released exclusively in Japan for
Shogi
Form of logic that allows quantification over predicates
definable by second-order formulas with an added transitive closure operator. EXPTIME is the set of languages definable by second-order formulas with an added
Second-order_logic
Concept in computer science
Babai, Lance Fortnow, Noam Nisan, and Avi Wigderson showed that unless EXPTIME collapses to MA, BPP is contained in i.o.-SUBEXP = ⋂ ε > 0 i.o.-DTIME (
BPP_(complexity)
Type of decision problem in computer science
other generalized games, such as chess, checkers (draughts), and Go are EXPTIME-complete because a game between two perfect players can be very long, so
PSPACE-complete
is a relativized universe (see oracle machine) where P = ⊕P ≠ NP = PP = EXPTIME, as shown by Beigel, Buhrman, and Fortnow in 1998. While Toda's theorem
Parity_P
Juris Hartmanis, Neil Immerman, Vivian Sewelson. Sparse Sets in NP-P: EXPTIME versus NEXPTIME. Information and Control, volume 65, issue 2/3, pp.158–181
Sparse_language
Set of problems solved by small circuits
#P-completeness of permanent. If EXPTIME ⊆ P/poly then E X P T I M E = Σ 2 P ∩ Π 2 P {\displaystyle {\mathsf {EXPTIME}}=\Sigma _{2}^{\mathsf {P}}\cap \Pi
P/poly
Type of automaton
Ladner, Lipton and Stockmeyer proved that this model is equivalent to EXPTIME i.e. a language is accepted by some APDA if, and only if, it can be decided
Pushdown_automaton
Extension of nondeterministic tree automaton
for ATAs, and therefore its complement, the universality problem, are EXPTIME-complete. The membership problem (testing whether an input tree is accepted
Alternating_tree_automata
Method for solving one problem using another
other complexity classes, including the PSPACE-complete languages and EXPTIME-complete languages. Every decision problem in P (the class of polynomial-time
Polynomial-time_reduction
Count solutions to an NP problem #P-complete The hardest problems in #P 2-EXPTIME Solvable in doubly exponential time AC0 A circuit complexity class of bounded
List_of_complexity_classes
Computer hardware and software capable of playing chess
arbitrarily large number of pieces on an arbitrarily large chessboard) is EXPTIME-complete, meaning that determining the winning side in an arbitrary position
Computer_chess
Number of cops needed to catch a robber on a graph
{\displaystyle O(n^{c})} , is true. Computing the cop number of a given graph is EXPTIME-hard, and hard for parameterized complexity. The cop-win graphs are the
Cop_number
Playing of contract bridge with computer software
has been proven EXPTIME-complete (both in EXPTIME and EXPTIME-hard), effectively meaning that it is among the hardest problems in EXPTIME. However, since
Computer_bridge
Declarative logic programming language
programs. With respect to program complexity, the decision problem is EXPTIME-complete. In particular, evaluating Datalog programs always terminates;
Datalog
Branch of mathematical logic
polynomial space. Second-order logic with a least fixed point operator gives EXPTIME, the problems solvable in exponential time. HO, the complexity class defined
Descriptive_complexity_theory
Computer science concept
higher levels of the polynomial hierarchy can be found in this Compendium. EXPTIME Exponential hierarchy Arithmetic hierarchy Arora, Sanjeev; Barak, Boaz
Polynomial_hierarchy
Extension of propositional modal logic
_{a\in A}[a]Z\right)} Satisfiability of a modal μ-calculus formula is EXPTIME-complete. Like for linear temporal logic, the model checking, satisfiability
Modal_μ-calculus
Abstract computation model
exponential time These are similar to the definitions of P, PSPACE, and EXPTIME, considering the resources used by an ATM rather than a deterministic Turing
Alternating_Turing_machine
Class in computational complexity theory
problem in P. If the number of steps is written in binary, the problem is EXPTIME-complete. This problem illustrates a common trick in the theory of P-completeness
P-complete
n = 1 {\displaystyle n=1} n ≥ 2 {\displaystyle n\geq 2} with common knowledge K, S4 PSPACE PSPACE EXPTIME KD45 NP PSPACE EXPTIME S5 NP PSPACE EXPTIME
Dynamic_epistemic_logic
Overview of and topical guide to algorithms
multipole method P (complexity) NP (complexity) NP-completeness NP-hardness EXPTIME PSPACE BPP (complexity) BQP Undecidable problem Halting problem Rice's
Outline_of_algorithms
Extension of Datalog
doi:10.1145/502807.502810. ISSN 0360-0300.. "For example, datalog (which is EXPTIME-complete) with linear arithmetic constraints [...] is undecidable." (Theorem
DatalogZ
Formal language concept
accepted by A is a subset of the words accepted by B is EXPTIME-complete. It is also EXPTIME-complete to figure out if there is a word that is not accepted
Nested_word
Concept in computability theory
Primitive recursive function Grzegorczyk hierarchy LOOP (programming language) EXPTIME Kalmár 1943. Kleene 1952, pp. 285, 526. Rose 1984, p. 3, Definition. Rose
Elementary_recursive_function
Topics referred to by the same term
a task with time complexity roughly proportional to such a function 2-EXPTIME, the complexity class of decision problems solvable in double-exponential
Double_exponential
left-concatenation and union and proved that their satisfiability problem is EXPTIME-complete. Conway proposed the following problem: given a constant finite
Language_equation
2009 book by Robert Hearn and Erik Demaine
is NP-complete, Rush Hour and reversi are PSPACE-complete, and chess is EXPTIME-complete. Beyond proving new results along these lines, the book aims to
Games, Puzzles, and Computation
Games,_Puzzles,_and_Computation
not mean that the class is low for itself. An example of such a class is EXPTIME, which is closed under complement, but is not low for itself. Some of the
Low_(complexity)
Complexity class from interactive proofs
subsumes a previous result of Kitaev and Watrous that QIP is contained in EXPTIME because QIP = QIP[3], so that more than three rounds are never necessary
IP_(complexity)
EXPTIME
EXPTIME
EXPTIME
EXPTIME
Girl/Female
Arabic, Australian, German, Hebrew, Muslim, Swedish
Born at Night; Night; Dark Beauty
Female
English
Probably an English variant spelling of German Wilma, VELMA means "will-helmet."Â
Girl/Female
Tamil
Arshia | à®…à®°à¯à®·à®¿à®¯à®¾
Heavenly
Girl/Female
German
Boldest
Boy/Male
British, English
From the Wildcat Brook
Girl/Female
German, Hebrew
God is Gracious; Female Version of Joan
Boy/Male
Indian, Tamil
Handsome
Boy/Male
Indian
Strong; Big
Boy/Male
Muslim/Islamic
Rising Standing, Existing, well-grounded
Female
Egyptian
, Set Amen, Daughter of the Sun.
EXPTIME
EXPTIME
EXPTIME
EXPTIME
EXPTIME