en>Limit-theorem: Switched the order of the derivations since the first easier and the second more formal.

2013-10-30T13:42:34Z

Switched the order of the derivations since the first easier and the second more formal.

← Older revision		Revision as of 15:42, 30 October 2013
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	~~I would like to introduce myself to you~~, ~~I am Andrew and my wife doesn~~'~~t like it at~~ all. ~~One~~ of the ~~things she loves most~~ is ~~canoeing and she's been doing it for quite~~ a ~~while~~. ~~He works as a bookkeeper~~. ~~Her family life~~ in ~~Ohio~~.<br><br>~~Review my web site~~ ... ~~psychic solutions by lynne~~ - [http://~~ustanford~~.~~com~~/~~index~~.~~php?do~~=/~~profile-38218/info/ browse around this web-site~~],		In [[computational complexity theory]], the [[complexity class]] '''2-EXPTIME''' (sometimes called '''2-EXP''') is the [[Set (mathematics)\|set]] of all [[decision problem]]s solvable by a [[deterministic Turing machine]] in [[big O notation\|O]](2<sup>2<sup>''p''(''n'')</sup></sup>) time, where ''p''(''n'') is a polynomial function of ''n''.

			In terms of [[DTIME]],

			:<math> \mbox{2-EXPTIME} = \bigcup_{k \in \mathbb{N} } \mbox{ DTIME } \left( 2^{ 2^{n^k} } \right) . </math>

			We know

			:[[P (complexity)\|P]] <math>\subseteq</math> [[NP (complexity)\|NP]] <math>\subseteq</math> [[PSPACE]] <math>\subseteq</math>[[EXPTIME]] <math>\subseteq</math> [[NEXPTIME]] <math>\subseteq</math> [[EXPSPACE]] <math>\subseteq</math> 2-EXPTIME <math>\subseteq</math> [[ELEMENTARY]].

			2-EXPTIME can also be reformulated as the space class AEXPSPACE, the problems that can be solved by an [[alternating Turing machine]] in exponential space. This is one way to see that EXPSPACE <math>\subseteq</math> 2-EXPTIME, since an alternating Turing machine is at least as powerful as a deterministic Turing machine.<ref>Christos Papadimitriou, Computational Complexity (1994), ISBN 978-0-201-53082-7. Section 20.1, corollary 3, page 495.</ref>

			2-EXPTIME is one class in a hierarchy of complexity classes with increasingly higher time bounds. The class 3-EXPTIME is defined similarly to 2-EXPTIME but with a triply exponential time bound <math>2^{2^{2^{n^k}}}</math>. This can be generalized to higher and higher time bounds.

			==2-EXPTIME-complete problems==

			Generalizations of many fully observable games are EXPTIME-complete. These games can be viewed as particular instance of a class of transition systems defined in terms of a set of state variables and actions/events that change the values of the state variables, together with the question of whether a winning strategy exists.

			A generalization of this class of fully observable problems to partially observable problems lifts the complexity from [[EXPTIME]]-complete to 2-EXPTIME-complete.<ref>{{ cite journal \| author = Jussi Rintanen \| title = Complexity of Planning with Partial Observability \| journal = Proceedings of International Conference on Automated Planning and Scheduling \| publisher = AAAI Press \| pages = 345–354 \| year = 2004 \| url=http://www.informatik.uni-freiburg.de/~ki/papers/Rintanen03compl.pdf}}</ref>

			==See also==
			* [[Double exponential function]]

			==References==
			<references/>

			{{ComplexityClasses}}

			[[Category:Complexity classes]]

en>Henrickunit: /* Derivation using Linear Approximation */

2011-11-27T02:22:42Z

Derivation using Linear Approximation

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I would like to introduce myself to you, I am Andrew and my wife doesn't like it at all. One of the things she loves most is canoeing and she's been doing it for quite a while. He works as a bookkeeper. Her family life in Ohio.<br><br>Review my web site ... psychic solutions by lynne - [http://ustanford.com/index.php?do=/profile-38218/info/ browse around this web-site],

Binomial approximation - Revision history

en>Limit-theorem: Switched the order of the derivations since the first easier and the second more formal.

en>Henrickunit: /* Derivation using Linear Approximation */