Ensemble interpretation - Revision history

en>Christian75: fix {{Quantum mechanics|Interpretations}}

2014-11-20T19:32:07Z

fix {{Quantum mechanics|Interpretations}}

← Older revision		Revision as of 21:32, 20 November 2014
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	~~{{DISPLAYTITLE:TC<sup>0</sup>}}~~		The author's name is Andera and she believes it seems quite good. My working day occupation is an info officer but I've already applied for another one. What me and my family members love is to climb but I'm thinking on starting some thing new. Ohio is exactly where my house is but my husband wants us to move.<br><br>My web site psychics online - [http://www.taehyuna.net/xe/?document_srl=78721 explanation] -
	~~'''TC<sup>0</sup>''~~' is ~~a [[complexity class]] used in [[circuit complexity]]~~. It is ~~the first class in the hierarchy of [[TC (complexity)\|TC]] classes~~.

	~~TC<sup>0</sup> contains all languages which are decided by [[Boolean circuit]]s with constant depth~~ and ~~polynomial size, containing only unbounded-fanin [[AND gate]]s, [[OR gate]]s, and [[majority gate]]s~~. ~~Equivalently, [[threshold gate]]s can be used instead of majority gates~~.

	TC<~~sup~~>0<~~/sup~~> ~~contains several important problems, such as sorting ''n'' ''n''~~-bit numbers, and multiplying two ''n''-bit numbers, integer division,<ref>{{cite journal\|first1=William\|last1=Hesse\|first2=Eric\|last2=Allender\|first3=David\|last3=Mix Barrington\|title=Uniform constant-depth threshold circuits for division and iterated multiplication\|journal=Journal of Computer and System Sciences\|volume=65\|year=2002\|pages=695–716\|doi=10.1016/S0022-0000(02)00025-9\|url=http://~~ftp.cs~~.~~rutgers~~.~~edu/pub/allender~~/~~division.pdf}}<~~/~~ref> recognizing the [[Dyck language]] with two types of parentheses.~~

	~~==Complexity class relations=~~=
	~~We can relate TC<sup>0</sup> to other circuit classes, including [[AC0\|AC<sup>0</sup>]] and [[NC1 (complexity)\|NC<sup>1</sup>]]; Vollmer 1999 p. 126 states:~~
	~~<blockquote>~~
	~~<math>\mbox{AC}^0 \subsetneq \mbox{AC}^0[p] \subsetneq \mbox{TC}^0 \subseteq \mbox{NC}^1. </math>~~
	~~</blockquote>~~
	~~Vollmer states that the question of whether the last inclusion above is strict is "one of the main open problems in circuit complexity" (ibid.).~~

	~~We also have that uniform <math>\mbox{TC}^0 \subsetneq \mbox{PP}</math>. (Allender 1996, as cited in Burtschick 1999).~~

	~~==References==~~
	~~{{reflist}}~~
	*{{cite book \| first=E. \| last=Allender \| chapter= A note on uniform circuit lower bounds for the counting hierarchy \| title=Proceedings 2nd International Computing and Combinatorics Conference (COCOON) \| volume=1090 \| series=Springer Lecture Notes in Computer Science \| pages=127–135 \| year=1996 }}
	*{{cite book \| last1=Clote \| first1=Peter \| last2=Kranakis \|first2=Evangelos \| title=Boolean functions and computation models \| series=Texts in Theoretical Computer Science. An EATCS Series \| location=Berlin \| publisher=[[Springer-Verlag]] ~~\| year=2002 \| isbn=3-540-59436~~-~~1 \| zbl=1016.94046 }}~~
	*{{cite book \| last = Vollmer \| first = Heribert \| title = Introduction to Circuit Complexity. A uniform approach \| series=Texts in Theoretical Computer Science \| year = 1999 \| publisher = [[Springer-Verlag]] \| location = Berlin \| isbn = 3-540-64310-9 \| zbl=0931.68055 }}
	*{{Cite journal \| last1 = Burtschick \| first1 = Hans-Jörg \| first2 = Heribert \| last2= Vollmer \| title = Lindström Quantifiers and Leaf Language Definability \| id={{ECCC\|1996\|96\|005}}\| year = 1999}}

	~~==External links==~~
	*{{CZoo\|TC<sup>0</sup>\|T#tc0}}

	~~{{ComplexityClasses}}~~

	~~[[Category:Circuit complexity]]~~
	~~[[Category:Complexity classes]]~~

en>Riddleh: changed "fundamental principal" to "fundamental principle"

2014-01-03T09:10:04Z

changed "fundamental principal" to "fundamental principle"

← Older revision		Revision as of 11:10, 3 January 2014
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	~~Hi there. Allow me begin by introducing the writer, her title~~ is ~~Myrtle Cleary~~. ~~North Dakota~~ is ~~our beginning place~~. ~~What I adore doing is playing baseball but I haven't produced a dime~~ with it. ~~Since she was eighteen she'~~s ~~been working as a receptionist but her promotion by no means arrives~~.<br><br>~~my page :: [~~http://cs.~~sch~~.ac.kr/xe/~~index~~.~~php?document_srl~~=~~1203900&mid~~=~~Game13 std home test~~]		{{DISPLAYTITLE:TC<sup>0</sup>}}
			'''TC<sup>0</sup>''' is a [[complexity class]] used in [[circuit complexity]]. It is the first class in the hierarchy of [[TC (complexity)\|TC]] classes.

			TC<sup>0</sup> contains all languages which are decided by [[Boolean circuit]]s with constant depth and polynomial size, containing only unbounded-fanin [[AND gate]]s, [[OR gate]]s, and [[majority gate]]s. Equivalently, [[threshold gate]]s can be used instead of majority gates.

			TC<sup>0</sup> contains several important problems, such as sorting ''n'' ''n''-bit numbers, and multiplying two ''n''-bit numbers, integer division,<ref>{{cite journal\|first1=William\|last1=Hesse\|first2=Eric\|last2=Allender\|first3=David\|last3=Mix Barrington\|title=Uniform constant-depth threshold circuits for division and iterated multiplication\|journal=Journal of Computer and System Sciences\|volume=65\|year=2002\|pages=695–716\|doi=10.1016/S0022-0000(02)00025-9\|url=http://ftp.cs.rutgers.edu/pub/allender/division.pdf}}</ref> recognizing the [[Dyck language]] with two types of parentheses.

			==Complexity class relations==
			We can relate TC<sup>0</sup> to other circuit classes, including [[AC0\|AC<sup>0</sup>]] and [[NC1 (complexity)\|NC<sup>1</sup>]]; Vollmer 1999 p. 126 states:
			<blockquote>
			<math>\mbox{AC}^0 \subsetneq \mbox{AC}^0[p] \subsetneq \mbox{TC}^0 \subseteq \mbox{NC}^1. </math>
			</blockquote>
			Vollmer states that the question of whether the last inclusion above is strict is "one of the main open problems in circuit complexity" (ibid.).

			We also have that uniform <math>\mbox{TC}^0 \subsetneq \mbox{PP}</math>. (Allender 1996, as cited in Burtschick 1999).

			==References==
			{{reflist}}
			*{{cite book \| first=E. \| last=Allender \| chapter= A note on uniform circuit lower bounds for the counting hierarchy \| title=Proceedings 2nd International Computing and Combinatorics Conference (COCOON) \| volume=1090 \| series=Springer Lecture Notes in Computer Science \| pages=127–135 \| year=1996 }}
			*{{cite book \| last1=Clote \| first1=Peter \| last2=Kranakis \|first2=Evangelos \| title=Boolean functions and computation models \| series=Texts in Theoretical Computer Science. An EATCS Series \| location=Berlin \| publisher=[[Springer-Verlag]] \| year=2002 \| isbn=3-540-59436-1 \| zbl=1016.94046 }}
			*{{cite book \| last = Vollmer \| first = Heribert \| title = Introduction to Circuit Complexity. A uniform approach \| series=Texts in Theoretical Computer Science \| year = 1999 \| publisher = [[Springer-Verlag]] \| location = Berlin \| isbn = 3-540-64310-9 \| zbl=0931.68055 }}
			*{{Cite journal \| last1 = Burtschick \| first1 = Hans-Jörg \| first2 = Heribert \| last2= Vollmer \| title = Lindström Quantifiers and Leaf Language Definability \| id={{ECCC\|1996\|96\|005}}\| year = 1999}}

			==External links==
			*{{CZoo\|TC<sup>0</sup>\|T#tc0}}

			{{ComplexityClasses}}

			[[Category:Circuit complexity]]
			[[Category:Complexity classes]]

en>Helpful Pixie Bot: ISBNs (Build KC)

2012-05-06T00:15:53Z

ISBNs (Build KC)

New page

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