Effective atomic number - Revision history

en>Arjayay: Rm "For" (included in template so appears as For For)

2014-10-15T13:02:12Z

Rm "For" (included in template so appears as For For)

← Older revision		Revision as of 15:02, 15 October 2014
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	~~In [[computational complexity theory]]~~ the '~~''compression theorem''' is an important theorem about the complexity of [[computable function]]~~s.		Greetings. Let me begin by telling you the author's title - Phebe. The preferred pastime for my kids and me is to play baseball but I haven't produced a dime with it. North Dakota is exactly where me and my husband reside. Bookkeeping is what I do.<br><br>Here is my weblog ... [http://www.hurtdating.com/groups/candida-albicans-tips-you-have-to-remember/ at home std testing]

	The ~~theorem states that there exists no largest [[complexity class]],~~ with ~~computable boundary, which contains all computable functions~~.

	~~==Compression theorem==~~
	~~Given a [[Gödel numbering]] <math>\varphi</math> of the computable functions~~ and ~~a [[Blum complexity measure]] <math>\Phi</math> where a complexity class for a boundary function~~ <~~math~~>f<~~/math~~> is ~~defined as~~
	~~:<math>\mathrm{C}(f):= \{\varphi_i \in \mathbf{R}^{(1)} \| (\forall^\infty x) \, \Phi_i (x) \leq f(x) \}~~.~~</math>~~

	~~Then there exists a [[total computable function]] <math>f</math> so that for all <math>i</math>~~
	~~:<math>\mathrm{Dom}(\varphi_i) = \mathrm{Dom}(\varphi_{f(i)})</math>~~
	~~and~~
	~~:<math>\mathrm{C}(\varphi_i) \subsetneq \mathrm{C}(\varphi_{f(i)})~~.~~</math>~~

	~~==References==~~
	*{{citation\|title=Computation and Automata\|volume=25\|series=Encyclopedia of Mathematics and Its Applications\|first=Arto\|last=Salomaa\|authorlink=Arto Salomaa\|publisher=Cambridge University Press\|year=1985\|isbn=9780521302456\|contribution=Theorem 6.~~9\|pages=149–150\|url=~~http://~~books~~.~~google~~.com/~~books?id=IblDi626fBAC&pg=PA149}}.~~
	*{{citation\|title=Computational Complexity: A Quantitative Perspective\|volume=196\|series=North-~~Holland Mathematics Studies\|first=Marius\|last=Zimand\|publisher=Elsevier\|year=2004\|isbn=9780444828415\|contribution=Theorem 2.4.3 (Compression theorem)\|page=42\|url=http:~~/~~/books.google.com/books?id=j-nhMYoZhgYC&pg=PA42}}.~~

	~~{{DEFAULTSORT:Compression Theorem}}~~
	~~[[Category:Computational complexity theory]]~~
	~~[[Category:Structural complexity theory]]~~
	~~[[Category:Theorems in the foundations of mathematics]~~]

en>Thibbs: Generalizing Britishism per WP:VNE

2013-07-14T14:11:20Z

Generalizing Britishism per WP:VNE

← Older revision		Revision as of 16:11, 14 July 2013
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	~~Alyson is what my spouse enjoys to call me but I don~~'~~t like when individuals use my full name. He~~ is an ~~information officer. For many years she'~~s ~~been residing in Kentucky but her spouse wants them to move~~. ~~What me and my family love is to climb~~ [~~http://www~~.~~zavodpm.ru~~/~~blogs~~/~~glennmusserrvji~~/~~14565-great-hobby-advice-assist-allow-you-get-going best psychic] but I'm psychic chat online~~ (~~[https~~:~~//www~~.~~machlitim.org.il~~/~~subdomain~~/~~megila~~/~~end/node/12300 www.machlitim.org.il]~~) ~~thinking on beginning some thing new.~~<br><br>~~Feel free to visit my web blog: best psychic readings~~ ([http://~~www~~.~~january-yjm~~.com/~~xe/index.php~~?~~mid~~=~~video~~&~~document_srl~~=~~158289 www~~.~~january~~-~~yjm~~.com])		In [[computational complexity theory]] the '''compression theorem''' is an important theorem about the complexity of [[computable function]]s.

			The theorem states that there exists no largest [[complexity class]], with computable boundary, which contains all computable functions.

			==Compression theorem==
			Given a [[Gödel numbering]] <math>\varphi</math> of the computable functions and a [[Blum complexity measure]] <math>\Phi</math> where a complexity class for a boundary function <math>f</math> is defined as
			:<math>\mathrm{C}(f):= \{\varphi_i \in \mathbf{R}^{(1)} \| (\forall^\infty x) \, \Phi_i (x) \leq f(x) \}.</math>

			Then there exists a [[total computable function]] <math>f</math> so that for all <math>i</math>
			:<math>\mathrm{Dom}(\varphi_i) = \mathrm{Dom}(\varphi_{f(i)})</math>
			and
			:<math>\mathrm{C}(\varphi_i) \subsetneq \mathrm{C}(\varphi_{f(i)}).</math>

			==References==
			*{{citation\|title=Computation and Automata\|volume=25\|series=Encyclopedia of Mathematics and Its Applications\|first=Arto\|last=Salomaa\|authorlink=Arto Salomaa\|publisher=Cambridge University Press\|year=1985\|isbn=9780521302456\|contribution=Theorem 6.9\|pages=149–150\|url=http://books.google.com/books?id=IblDi626fBAC&pg=PA149}}.
			*{{citation\|title=Computational Complexity: A Quantitative Perspective\|volume=196\|series=North-Holland Mathematics Studies\|first=Marius\|last=Zimand\|publisher=Elsevier\|year=2004\|isbn=9780444828415\|contribution=Theorem 2.4.3 (Compression theorem)\|page=42\|url=http://books.google.com/books?id=j-nhMYoZhgYC&pg=PA42}}.

			{{DEFAULTSORT:Compression Theorem}}
			[[Category:Computational complexity theory]]
			[[Category:Structural complexity theory]]
			[[Category:Theorems in the foundations of mathematics]]

en>Physics nuclear at 01:28, 22 March 2012

2012-03-22T01:28:59Z

New page

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