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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] |
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| The theorem states that there exists no largest [[complexity class]], with computable boundary, which contains all computable functions. | |
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| ==Compression theorem==
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| 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
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| :<math>\mathrm{C}(f):= \{\varphi_i \in \mathbf{R}^{(1)} | (\forall^\infty x) \, \Phi_i (x) \leq f(x) \}.</math>
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| Then there exists a [[total computable function]] <math>f</math> so that for all <math>i</math>
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| :<math>\mathrm{Dom}(\varphi_i) = \mathrm{Dom}(\varphi_{f(i)})</math>
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| and
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| :<math>\mathrm{C}(\varphi_i) \subsetneq \mathrm{C}(\varphi_{f(i)}).</math>
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| ==References==
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| *{{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}}.
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| *{{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}}.
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| {{DEFAULTSORT:Compression Theorem}}
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| [[Category:Computational complexity theory]]
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| [[Category:Structural complexity theory]]
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| [[Category:Theorems in the foundations of mathematics]]
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Latest revision as of 14:02, 15 October 2014
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.
Here is my weblog ... at home std testing