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Chaitin's constant - Wikipedia

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In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number)[1] or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt. These numbers are formed from a construction due to Gregory Chaitin. Although there are infinitely many halting probabilities, one for each method of encoding programs, it is common to use the letter Ω to refer to them as if there were only one. Because Ω depends on the program encoding used, it is sometimes called Chaitin's construction when not referring to any specific encoding. Each halting probability is a normal and transcendental real number that is not computable, which means that there is no algorithm to compute its digits. Each halting probability is Martin-Löf random, meaning there is not even any algorithm which can reliably guess its digits. The definition of a halting probability relies on the existence of a prefix-free un

Chaitin's constant - Wikipedia Jump to content From Wikipedia, the free encyclopedia Halting probability of a random computer program "Omega number" redirects here. For other uses, see Omega (disambiguation) § Mathematics . In the computer science subfield of algorithmic information theory , a Chaitin constant ( Chaitin omega number ) [ 1 ] or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt . These numbers are formed from a construction due to Gregory Chaitin . Although there are infinitely ma

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