PSPACE-complete - Revision history

en>Rjwilmsi: /* References */Journal cites, Added 1 doi to a journal cite using AWB (10331)

2014-08-08T06:36:56Z

References: Journal cites, Added 1 doi to a journal cite using AWB (10331)

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	In [~~[computational complexity theory\|complexity theory]~~], ~~'''EXPSPACE'''~~ is the ~~[[Set (mathematics)\|set]] of all [[decision problem]]s solvable by a deterministic [[Turing machine]] in [[big O notation\|O]](2~~<~~sup~~>~~''p''(''n'')</sup>) space~~, ~~where ''p''(''n'') is a polynomial function~~ of ~~''n''~~. ~~(Some authors restrict ''p''(''n'')~~ to ~~be a [[linear function]]~~, ~~but most authors instead call the resulting class '''[[ESPACE]]'''.) If we use a nondeterministic machine instead, we get the class '''NEXPSPACE'''~~, ~~which is equal to '''EXPSPACE''' by [[Savitch's theorem]]~~.		When buying flower gifts, you generally consider exactly what the occasion or celebration is about. No should anything, [https://fusechicken.Zendesk.com/entries/42192165-Lavender-Oil zendesk.com], visit the shops: This is one in the main great things about choosing same day flower delivery kolkata services.<br>If you live in or throughout the Ithaca, New York area, visit one of such highly recommend florists for many of your floral needs. One can send these flowers to his partner, lover, buddy or business associate and express his good plans toward them.<br><br>

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

	~~A decision problem is '''EXPSPACE~~-~~complete''' if it is in '''EXPSPACE''', and every problem in '''EXPSPACE''' has~~ a ~~[[polynomial~~-~~time many~~-~~one reduction]] to it. In other words, there is~~ a ~~polynomial~~-~~time [[algorithm]] that transforms instances of one to instances of the other with the same answer. '''EXPSPACE~~-~~complete''' problems might~~ be ~~thought~~ of ~~as the hardest problems in '''EXPSPACE'''~~.

	~~'''EXPSPACE''' is a strict superset of '''[[PSPACE~~]~~]''', '''[[NP (complexity)\|NP]]''', and '''[[P (complexity)\|P]]''' and~~ is ~~believed~~ to be a ~~strict superset~~ of ~~'''~~[~~[EXPTIME]]'''~~.

	~~An example of an '''EXPSPACE~~-~~complete''' problem is the problem of recognizing whether two [[regular expression]]s represent different languages, where the expressions are limited~~ to ~~four operators: union, [[concatenation~~]~~], the [[Kleene star]] (zero or more copies of~~ an ~~expression)~~, ~~and squaring~~ (~~two copies of~~ an ~~expression)~~.~~<ref>Meyer, A~~.~~R. and [[Larry Stockmeyer\|L. Stockmeyer~~]]. [http://~~people~~.~~csail~~.~~mit.edu~~/~~meyer~~/~~rsq.pdf The equivalence problem for regular expressions~~ with ~~squaring requires exponential space]~~. ~~''13th IEEE Symposium on Switching and Automata Theory'', Oct 1972, pp~~.~~125–129~~.</~~ref>~~

	~~If the Kleene star is left out, then that problem becomes '''[[NEXPTIME~~]~~]-complete''', which is like '''EXPTIME-complete'''~~, ~~except it is defined in terms of~~ [~~[non-deterministic Turing machine]]s rather than deterministic~~.

	~~It has also been shown by L~~. ~~Berman in 1980 that the problem of verifying~~/~~falsifying any [[first~~-~~order logic\|first~~-~~order]] statement about [[real number]]s that involves only [[addition]]~~ and ~~comparison (but no [[multiplication~~]~~]) is~~ in ~~'''EXPSPACE'''~~.

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

	~~== References ==~~

	~~<references />~~
	* ~~L. Berman ''The complexity of logical theories'', Theoretical Computer Science 11:71-78, 1980.~~
	* ~~{{cite book\|author = [[Michael Sipser]] \| year = 1997 \| title = Introduction~~ to the ~~Theory of Computation \| publisher = PWS Publishing \| isbn = 0-534-94728-X}} Section 9.1.1: Exponential space completeness~~, ~~pp. 313–317. Demonstrates that determining equivalence of regular expressions with exponentiation is EXPSPACE-complete~~.

	~~{{ComplexityClasses}}~~

	~~[[Category:Complexity classes]]~~

en>Yobot: WP:CHECKWIKI error fixes using AWB (9475)

2013-09-10T17:52:39Z

WP:CHECKWIKI error fixes using AWB (9475)

← Older revision		Revision as of 19:52, 10 September 2013
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	~~You want somebody who has an honest job along with~~ a ~~regular pay check. CCTV security products that provides good opportunity for service providers on this segment. The problems~~ of ~~wired CCTV are actually made solution through the wireless CCTV cameras~~. [~~http://www~~.~~fraservalleyguide.com/redirect.php?url=cctvdvrreviews.com how~~ to ~~connect your cctv dvr to the internet~~] ~~Some with the equipment works well for monitoring places and people remotely; via internet~~.~~<br><br>~~		In [[computational complexity theory\|complexity theory]], '''EXPSPACE''' is the [[Set (mathematics)\|set]] of all [[decision problem]]s solvable by a deterministic [[Turing machine]] in [[big O notation\|O]](2<sup>''p''(''n'')</sup>) space, where ''p''(''n'') is a polynomial function of ''n''. (Some authors restrict ''p''(''n'') to be a [[linear function]], but most authors instead call the resulting class '''[[ESPACE]]'''.) If we use a nondeterministic machine instead, we get the class '''NEXPSPACE''', which is equal to '''EXPSPACE''' by [[Savitch's theorem]].

	In the China electronics wholesale market, such multifunctional car digital camcorders are sold in bulk. This cupboard isnâ€™t relegated to your specific geographical region, or to some specific time zone or timeslot. People like the felling for being remembered and so [~~http~~:~~//www.cpu4u.com/redirect.php?action~~=~~url&goto~~=~~cctvdvrreviews.com cctv dvr explained] they really appreciate when we take out time to do something special on their behalf even~~ if ~~it indicates sending a single text message. Today car lovers and users can take advantage of unlimited facilities of their cars if they want and that also~~ it is ~~determined by their budget. Gone then will be the days of aimlessly scrolling though lines of text~~ and ~~website URL~~'~~s.<br><br>Remember, online “friends” may~~ '~~t be who they say they~~'~~re. Once~~ [~~http://trip~~-~~Review.ru/personal_blog/discussed/ installed~~] ~~correctly, you need not~~ to ~~touch the camera because you understand that~~ it ~~will keep recording for countless hours~~. ~~This feature~~ is ~~utilized by Biometric access control system~~ to ~~control access~~ of ~~different visitors to particular areas. CCTV has~~ other ~~practical applications beyond surveillance and CCTV networks don't necessarily feature video cameras. They know we now have~~ the ~~power to alter and regain our civil liberties and they are willing to do whatever it takes to be heard and not herd~~. ~~A CCTV security system is an excellent option for those who~~'~~ve property that has many different~~ '~~spaces~~' ~~that cannot all~~ be ~~observed at one time.<br><br>Phone bugs, GPS trackers, phone jamming devices and infrared binoculars are some with~~ the ~~other Surveillance Equipment~~. ~~More widely, there~~ is ~~also an underground metro system being constructed~~, ~~aimed to link-up towards the BRT this also is expected to get completed in time for that 2016 Olympics.<br><br>Well~~, it is ~~difficult~~ to ~~maneuver~~ a ~~wired camera according to your requirement~~. ~~If you need people to actually buy your product or service, make it along with your audience at heart. Security~~ is ~~fundamentally important across all walks~~ of ~~life~~ to ~~ensure~~ the ~~overall safety~~ and ~~possessions~~ of ~~most individuals are comprehensively protected~~.<br>~~<br>Contemporary recorders have the facility to playback recordings coming from a chosen location~~. ~~Apart from burglar alarm there is certainly yet another security system which is becoming extremely popular~~.~~<br><br>The maintenance price of the camera is just a little bit higher as opposed to wired CCTV~~. ~~The device is plugged directly into an Ethernet~~ [http://~~seo~~.~~fine~~.~~to/rank~~.~~cgi?mode=link&id=10512&url=http:~~//~~cctvdvrreviews~~.~~com cctv dvr internet viewer~~] ~~switch and the only way to access the device is via the network~~. ~~Chick lit is form frictions that address the modern issues of women independence, in a timid manner. And by continuing to keep my heart closed up tight~~ and ~~denying myself intimacy using this type of person~~, ~~I have been missing out on so much of the beauty that life must offer.<br><br>Additionally~~, ~~it is possible to record one program as you're watching another live~~. ~~You want somebody who has a nice relationship together with his parents. Then you'll need to purchase a BNC to Phono connector, and if necessary a scart connection~~.<br>~~<br>The recording program is vital for~~ the ~~reason that it~~ is ~~the proof a thief was involved having an unlawful activity. Be sure~~ that all cameras come with all the necessary power adaptors and suitable wall mounting kits.<br><br>For example, Sarah could also have taken care of immediately Erik with, “How long have you ever thought I didn'~~t care about Again (~~[~~http://www.senpolia.ru/link/?url=cctvdvrreviews.com http://www.senpolia.ru/~~]~~) you. We use a list of ten great options that provide everything from e~~-~~mail filtering to transforming your Android phone right into a remote control.<br><br>Check out the additional options as some allow backup onto CD burner~~, ~~USB ports or perhaps a network link in your PC. Find out more to do with each form of camera to determine~~ which ~~kind~~ is ~~most suitable for you.<br><br>So property managers should make sure they~~'~~re not~~ [~~http://C2687710~~.~~Myzen~~.~~Co.uk~~/~~groups/you~~-~~make~~-~~these-dvr-cctv-freeware-mistakes/ incurring~~] ~~any legal risks before establishing CCTV equipment. The apartments are breathtakingly spacious, open on all sides, giving an unfettered view with the green landscaped surroundings~~ and ~~simultaneously guaranteeing utmost privacy. Here are five with the most valuable lessons it~~ is possible to take from this show and apply with your life. You are busy going from work to getting your kids to after school activities. You determine if your objectives are actually met AFTER the $5000 has become spent.<~~br><br~~>The ~~most reliable way~~ of ~~doing that is through an automated technique of Disaster Recovery~~, ~~offsite data backup and hard disk recovery~~ to ~~make sure rapid and cost effective execution. Favorite shows can be recorded through~~ the ~~entire week and then enjoyed a single evening~~. ~~Horizontal resolution measures the quantity of elements making up each horizontal line~~. ~~However~~, ~~filters may also impair image quality and overall light sensitivity of cameras (see laser safety article for details on difficulty with filters)~~. ~~By using Modem and Cables also, boost the quality and fastest connection~~. ~~Direct tv next transmits most~~ of ~~these signs to a few satellites located in geostationary orbit~~.		In terms of '''[[DSPACE]]''' and '''[[NSPACE]]''',

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

			A decision problem is '''EXPSPACE-complete''' if it is in '''EXPSPACE''', and every problem in '''EXPSPACE''' has a [[polynomial-time many-one reduction]] to it. In other words, there is a polynomial-time [[algorithm]] that transforms instances of one to instances of the other with the same answer. '''EXPSPACE-complete''' problems might be thought of as the hardest problems in '''EXPSPACE'''.

			'''EXPSPACE''' is a strict superset of '''[[PSPACE]]''', '''[[NP (complexity)\|NP]]''', and '''[[P (complexity)\|P]]''' and is believed to be a strict superset of '''[[EXPTIME]]'''.

			An example of an '''EXPSPACE-complete''' problem is the problem of recognizing whether two [[regular expression]]s represent different languages, where the expressions are limited to four operators: union, [[concatenation]], the [[Kleene star]] (zero or more copies of an expression), and squaring (two copies of an expression).<ref>Meyer, A.R. and [[Larry Stockmeyer\|L. Stockmeyer]]. [http://people.csail.mit.edu/meyer/rsq.pdf The equivalence problem for regular expressions with squaring requires exponential space]. ''13th IEEE Symposium on Switching and Automata Theory'', Oct 1972, pp.125–129.</ref>

			If the Kleene star is left out, then that problem becomes '''[[NEXPTIME]]-complete''', which is like '''EXPTIME-complete''', except it is defined in terms of [[non-deterministic Turing machine]]s rather than deterministic.

			It has also been shown by L. Berman in 1980 that the problem of verifying/falsifying any [[first-order logic\|first-order]] statement about [[real number]]s that involves only [[addition]] and comparison (but no [[multiplication]]) is in '''EXPSPACE'''.

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

			== References ==

			<references />
			* L. Berman ''The complexity of logical theories'', Theoretical Computer Science 11:71-78, 1980.
			* {{cite book\|author = [[Michael Sipser]] \| year = 1997 \| title = Introduction to the Theory of Computation \| publisher = PWS Publishing \| isbn = 0-534-94728-X}} Section 9.1.1: Exponential space completeness, pp. 313–317. Demonstrates that determining equivalence of regular expressions with exponentiation is EXPSPACE-complete.

			{{ComplexityClasses}}

			[[Category:Complexity classes]]

en>Qetuth: /* Discussion */ fixed dablink

2011-12-28T23:53:22Z

Discussion: fixed dablink

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