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Topic: Chaitins constant

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	Kids.Net.Au - Encyclopedia > Chaitins constant (Site not responding. Last check: 2007-10-10)
		Chaitin's constant, Ω (capital omega), also called the halting probability, is a construction by Gregory Chaitin.
		It is important to realize that Chaitin's constant is not a constant in the usual sense: it is not a fixed, canonically defined number such as π or e since its definition depends on the arbitrary choice of computation model and program encoding.
		(The constant N heavily depends on the encoding choices and does not reflect the complexity of the axiomatic system in any way.) This is an incompleteness result akin to Gödel's incompleteness theorem and Chaitin's own result mentioned under algorithmic information theory.
	www.kids.net.au /encyclopedia-wiki/ch/Chaitins_constant (484 words)

	Chaitin’s Constant
		It has no pattern or structure to it whatsoever, but consists instead of an infinitely long string of 0's and 1's in which each digit is as unrelated to its predecessor as one coin toss is from the next.
		Although called a constant, it is not a constant in the sense that, for example, π is, since its definition depends on the arbitrary choice of computation model and programming language.
		To derive it, Chaitin considered all the possible programs that a hypothetical computer known as a Turing machine could run, and then looked for the probability that a program, chosen at random from among all the possible programs, will halt.
	www.daviddarling.info /encyclopedia/C/Chaitins_constant.html (529 words)

	download ac3 filter codec (Site not responding. Last check: 2007-10-10)
		In contrast to the strings shortest description in some cases a lossy pression algorithms (like MP3).
		Meanwhile there is slightly less uncertainty about the properties of Chaitins constant.
		The minimum message length principle of statistical mechanics and information theory to make things easier.
	ac3-codec-download.blogest.org /download-ac3-filter-codec--.html (628 words)

	Chaitin's constant : Chaitins constant
		Chaitin's constant, Ω (capital omega), also called the halting probability, is a construction by Gregory Chaitin.
		It is important to realize that Chaitin's constant isn't a constant in the usual sense: it isn't a fixed, canonically defined number such as π or e since its definition depends on the arbitrary choice of computation model and program encoding.
		(The constant N heavily depends on the encoding choices and doesn't reflect the complexity of the axiomatic system in any way.) This is an incompleteness result akin to Gödel's incompleteness theorem and Chaitin's own result mentioned under algorithmic information theory.
	www.wordlist.org /ch/chaitins-constant.html (524 words)

	A crank post about Chaitins constant (Site not responding. Last check: 2007-10-10)
		Chaitin, however, seems to be quite indifferent to all such criticism.
		Chaitin never mentions Rosser's theorem, but oddly continues to be referred to as having developed the "strongest possible version of Godel's Theorem".
		So the number of different Chaitins Constants we can make is equal to the number of mappings from N to N, which (I believe) is C. So there are an uncountable number of Chaitins constants.
	www.forum-one.org /new-2216633-4343.html (2007 words)

	Chaitin's constant (Site not responding. Last check: 2007-10-10)
		In the computer science subfield of algorithmic information theory the Chaitin constant or halting probability is a construction by Gregory Chaitin which describes the probability that a randomly generated program for a given model computation or programming language will halt.
		If you fix in addition to the model and encoding mentioned above a specific axiomatic system for the natural numbers say Peano's axioms then there exists a constant N such that no digit of Ω the N -th can be proven to be one zero within that system.
		(The constant N heavily depends on the encoding choices does not reflect the complexity of the system in any way.) This is an result akin to Gödel's incompleteness theorem and Chaitin's own result mentioned under algorithmic information theory.
	www.freeglossary.com /Chaitins_constant (644 words)

	sci.math: Re: Raatikainen's critique of Chaitin
		In reply to: Eray Ozkural exa: "Re: Raatikainen's critique of Chaitin"
		Re: Panu Raatikainens review of two of Chaitins books.
		We are proud to have Web Hosting and Rack Housing from 9 Net Avenue Deutschland.
	sci.tech-archive.net /Archive/sci.math/2004-09/0326.html (217 words)

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