Quantum logic - Revision history

86.183.223.225 at 16:42, 23 November 2014

2014-11-23T16:42:36Z

← Older revision		Revision as of 18:42, 23 November 2014
Line 1:		Line 1:
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en>AnomieBOT: Dating maintenance tags: {{Cn}}

2014-02-25T00:15:56Z

Dating maintenance tags: {{Cn}}

← Older revision		Revision as of 02:15, 25 February 2014
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	~~In [[computational complexity theory]]~~, the ~~[[complexity class]]~~ '''~~NEXPTIME''' (sometimes called '''NEXP''') is~~ the ~~set of [[decision problem]]s that can be solved by a [[non-deterministic Turing machine]] using time [[Big O notation\|O]](2~~<~~sup~~>~~''p''(n)~~<~~/sup~~>~~) for some [[polynomial]] ''p''(n), and unlimited space.~~		For anyone who is having trouble seeing a casino game while you are grinding it, try adjusting our own brightness environment. Might make the display look clear, enhancing your video game players expertise. And let's face it, you won't achieve any kind concerning success if you not able to see what you're doing, so make the golf game meet your needs.<br><br>

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	~~:<math>\mbox{NEXPTIME} = \bigcup_{k\in\mathbb{N}} \mbox{NTIME}(2^{n^k})</math>~~

	~~An important set of~~ '~~''NEXPTIME'''-complete problems relates~~ to ~~[[succinct circuit]]s~~. ~~Succinct circuits are simple machines used to describe graphs in exponentially less space. They accept two vertex numbers~~ as ~~input and output whether there is an edge between them~~. ~~If solving a problem on a graph~~ in ~~a natural representation, such as an [[adjacency matrix]], is [[NP-complete]], then solving~~ the ~~same problem on a succinct circuit representation is '''NEXPTIME'''-complete~~, ~~because~~ the ~~input is exponentially smaller (under some mild condition~~ that ~~the NP-completeness reduction is achieved by a "projection")~~.<~~ref~~>~~[[Christos Papadimitriou\|C. Papadimitriou]] & [[Mihalis Yannakakis\|M. Yannakakis]], ''A note on succinct representations~~ of ~~graphs''~~, ~~Information~~ and ~~control, vol 71 num 3, décember 1986, pp. 181—185, {{doi\|10.1016~~/~~S0019-9958(86)80009-2}}<~~/~~ref><ref>C~~. ~~Papadimitriou~~. ~~''Computational Complexity'' Addison~~-~~Wesley, 1994. ISBN 0~~-~~201-53082-1. Section 20.1~~, pg.~~492~~.~~</ref> As one simple example~~, ~~finding a [[Hamiltonian path]] for a graph thus encoded is '''NEXPTIME'''-complete.~~

	~~If [[P = NP problem\|'''P''' = '''NP''']], then '''NEXPTIME''' = '''EXPTIME''' ([[padding argument]]); more precisely, '''[[E (complexity)\|E]]''' ≠ '''[[NE (complexity)\|NE]]''' if~~ and ~~only if there exist [[sparse language]]s in '''NP'''~~ that ~~are not in '''P''~~'.<~~ref~~>~~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. 1985.~~ [~~http~~://~~portal~~.~~acm~~.~~org~~/~~citation.cfm~~?id=~~808769 At ACM Digital Library~~]~~</ref>~~

	~~== Alternative characterizations ==~~

	~~'''NEXPTIME''' often arises~~ in ~~the context of [[interactive proof system]]s~~, ~~where there are two major characterizations of it~~. The ~~first is the '''MIP''' proof system, where we~~ have ~~two all-powerful provers~~ which ~~communicate with a randomized polynomial-time verifier (but not with each other). If~~ the ~~string is~~ in the ~~language, they~~ must be ~~able to convince~~ the ~~verifier of this with high probability~~. If ~~the string is not in the language~~, ~~they must not~~ be ~~able to collaboratively trick~~ the ~~verifier into accepting the string except with low probability. The fact that '''MIP''' proof systems can solve every problem in '''NEXPTIME''' is quite impressive when we consider that when only~~ one ~~prover is present~~, ~~we can only recognize all of~~ '~~''PSPACE''';~~ the ~~verifier~~'~~s ability~~ to ~~"cross-examine"~~ the ~~two provers gives it great power~~. ~~See [[interactive proof system#MIP]] for more details.~~

	~~Another interactive proof system characterizing '''NEXPTIME'''~~ is ~~a certain class of [[probabilistically 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 ~~the language~~, and ~~a deterministic polynomial-time machine verifies that it is a valid proof~~. ~~We make two changes~~ to ~~this setup:~~

	* Add randomness, ~~the ability to flip coins~~, to the ~~verifier machine~~.
	* Instead of simply giving the purported proof to ~~the verifier on a tape, give it random~~ access to the ~~proof. The verifier can specify an index into the proof string and receive the corresponding bit. Since the verifier can write an index~~ of ~~polynomial length, it can potentially index into an exponentially long proof string.~~

	~~These two extensions together greatly extend the proof system~~'s ~~power, enabling it to recognize all languages in '''NEXPTIME'''~~. ~~The class is called '''PCP'''(poly, poly)~~. ~~What more~~, ~~in this characterization the verifier may be limited to read only a constant number of bits~~, ~~i.e. '''NEXPTIME''' = '''PCP'''(poly~~, ~~1). See [[probabilistically checkable proof]]s for more details~~.

	~~==See also==~~
	*[[Game complexity]]

	~~==References==~~
	~~<references/>~~

	* {{CZoo\|NEXP\|N#nexp}}, {{CZoo\|coNEXP\|C#conexp}}

	~~{{ComplexityClasses}}~~

	~~{{DEFAULTSORT:Nexptime}}~~
	~~[[Category:Complexity classes]]~~

en>MorphismOfDoom: Removed claim that QL approach can be subsumed by Cstar algebraic w/ minor technical assumptions since it's dubious, not supported with citations and not mentioned again in the article.

2014-01-29T03:35:03Z

Removed claim that QL approach can be subsumed by Cstar algebraic w/ minor technical assumptions since it's dubious, not supported with citations and not mentioned again in the article.

← Older revision		Revision as of 05:35, 29 January 2014
Line 1:		Line 1:
	~~A person of~~ the ~~prevalent issue about which you may possibly have heard~~ of ~~would~~ be ~~hiding age~~.<br>~~To conceal age people are earning use~~ of ~~anti aging product~~. ~~The tendency of growing old is superior among ladies as when compared~~ to ~~that of adult males~~. ~~These are the form of products that are out~~ there in ~~greater part of~~ the ~~beauty stores.<br>Majority of~~ the ~~moments growing old signals are visible all around mouth as nicely as eyes. One detail that you need to know~~ is that the ~~pores and skin near the eye as well as mouth~~ is ~~extremely delicate~~ and ~~so it gets impacted initially~~. ~~This is the skin that has considerably less amount of dampness~~.<br><br>~~There are innumerable models that have produced a number of anti growing older as very well as anti wrinkle lotions~~.<br>~~It is necessary~~ for ~~you to know which anti getting old cream~~ is ~~acceptable to your pores~~ and ~~skin~~. At the time ~~of choosing these lotions you will need to~~ be ~~remarkably cautious with regards~~ to the ~~components made use~~ of ~~in the lotions~~. ~~In scenario~~ the ~~product~~ is not ~~acceptable it can guide to allergy which can verify to~~ be ~~harmful.<br>There are moments when you appear~~ to ~~know about no matter whether~~ the ~~product suits you or not only following you have used it.<br><br>There are anti wrinkle creams obtainable for~~ the ~~eyes that help in eradicating darkish circles, eye baggage as nicely as wrinkles~~. The ~~creams~~ that ~~are normally designed for the getting older are the kinds~~ that ~~will comprise~~ of ~~oil glands which will hydrate~~ the ~~pores and skin and make~~ it ~~very sleek~~.~~<br>As you age you will are likely to get a lot~~ more ~~wrinkles~~. ~~This~~ is ~~when anti wrinkle creams are made use~~ of ~~which~~ can be ~~beneficial for pores and skin~~ of the ~~confront~~. ~~These are~~ the ~~creams that comprise of~~ the ~~component which is lessening down wrinkles as properly as make your pores and skin organization~~.~~<br><br>You can also lessen down the freckles from your confront by earning use~~ of ~~these lotions. At~~ the ~~time of purchasing these anti getting older lotions then~~ the ~~foremost issue~~ on ~~which you want~~ to ~~pay back focus is~~ the ~~high quality of~~ the ~~creams~~. ~~This is since~~ the ~~creams that are~~ of ~~very low high-quality~~ can ~~guide to skin damages.<br>If you cherished this informative article and also you want to be given more details about dermology anti-wrinkle cream ([http://fanbuzzy.com/~~index.~~php?do=/profile-7482/info/ fanbuzzy.com]) generously check out~~ the ~~web page~~. The ~~very low excellent creams can lead to rashes~~, ~~pimples as nicely as scars above the encounter~~. ~~There are moments when pores and skin can experience irritation as very well as itchiness. To get~~ the ~~greatest outcomes you need~~ to ~~make~~ a ~~smart choice~~ for ~~merchandise~~.<br>~~<br>It is important for you to select anti getting older with the word of mouth. Via this you will be capable to get rid of your difficulties understanding better lotions of excellent outcomes.~~		In [[computational complexity theory]], the [[complexity class]] '''NEXPTIME''' (sometimes called '''NEXP''') is the set of [[decision problem]]s that can be solved by a [[non-deterministic Turing machine]] using time [[Big O notation\|O]](2<sup>''p''(n)</sup>) for some [[polynomial]] ''p''(n), and unlimited space.

			In terms of [[NTIME]],

			:<math>\mbox{NEXPTIME} = \bigcup_{k\in\mathbb{N}} \mbox{NTIME}(2^{n^k})</math>

			An important set of '''NEXPTIME'''-complete problems relates to [[succinct circuit]]s. Succinct circuits are simple machines used to describe graphs in exponentially less space. They accept two vertex numbers as input and output whether there is an edge between them. If solving a problem on a graph in a natural representation, such as an [[adjacency matrix]], is [[NP-complete]], then solving the same problem on a succinct circuit representation is '''NEXPTIME'''-complete, because the input is exponentially smaller (under some mild condition that the NP-completeness reduction is achieved by a "projection").<ref>[[Christos Papadimitriou\|C. Papadimitriou]] & [[Mihalis Yannakakis\|M. Yannakakis]], ''A note on succinct representations of graphs'', Information and control, vol 71 num 3, décember 1986, pp. 181—185, {{doi\|10.1016/S0019-9958(86)80009-2}}</ref><ref>C. Papadimitriou. ''Computational Complexity'' Addison-Wesley, 1994. ISBN 0-201-53082-1. Section 20.1, pg.492.</ref> As one simple example, finding a [[Hamiltonian path]] for a graph thus encoded is '''NEXPTIME'''-complete.

			If [[P = NP problem\|'''P''' = '''NP''']], then '''NEXPTIME''' = '''EXPTIME''' ([[padding argument]]); more precisely, '''[[E (complexity)\|E]]''' ≠ '''[[NE (complexity)\|NE]]''' if and only if there exist [[sparse language]]s in '''NP''' that are not in '''P'''.<ref>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. 1985. [http://portal.acm.org/citation.cfm?id=808769 At ACM Digital Library]</ref>

			== Alternative characterizations ==

			'''NEXPTIME''' often arises in the context of [[interactive proof system]]s, where there are two major characterizations of it. The first is the '''MIP''' proof system, where we have two all-powerful provers which communicate with a randomized polynomial-time verifier (but not with each other). If the string is in the language, they must be able to convince the verifier of this with high probability. If the string is not in the language, they must not be able to collaboratively trick the verifier into accepting the string except with low probability. The fact that '''MIP''' proof systems can solve every problem in '''NEXPTIME''' is quite impressive when we consider that when only one prover is present, we can only recognize all of '''PSPACE'''; the verifier's ability to "cross-examine" the two provers gives it great power. See [[interactive proof system#MIP]] for more details.

			Another interactive proof system characterizing '''NEXPTIME''' is a certain class of [[probabilistically 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 the language, and a deterministic polynomial-time machine verifies that it is a valid proof. We make two changes to this setup:

			* Add randomness, the ability to flip coins, to the verifier machine.
			* Instead of simply giving the purported proof to the verifier on a tape, give it random access to the proof. The verifier can specify an index into the proof string and receive the corresponding bit. Since the verifier can write an index of polynomial length, it can potentially index into an exponentially long proof string.

			These two extensions together greatly extend the proof system's power, enabling it to recognize all languages in '''NEXPTIME'''. The class is called '''PCP'''(poly, poly). What more, in this characterization the verifier may be limited to read only a constant number of bits, i.e. '''NEXPTIME''' = '''PCP'''(poly, 1). See [[probabilistically checkable proof]]s for more details.

			==See also==
			*[[Game complexity]]

			==References==
			<references/>

			* {{CZoo\|NEXP\|N#nexp}}, {{CZoo\|coNEXP\|C#conexp}}

			{{ComplexityClasses}}

			{{DEFAULTSORT:Nexptime}}
			[[Category:Complexity classes]]

92.4.132.247 at 19:24, 4 August 2012

2012-08-04T19:24:11Z

New page

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