Chaitin's Constant
In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that informally 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, 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 instead of Chaitin's constant when not referring to any specific encoding.
Each halting probability is a normal and transcendental real number which is not computable, which means that there is no algorithm that enumerates its digits.
Read more about Chaitin's Constant: Background, Definition, Relationship To The Halting Problem, Interpretation As A Probability, Properties, Uncomputability, Incompleteness Theorem For Halting Probabilities, Super Omega
Famous quotes containing the word constant:
“Guilty, guilty, guilty is the chant divorced parents repeat in their heads. This constant reminder remains just below our consciousness. Nevertheless, its presence clouds our judgment, inhibits our actions, and interferes in our relationship with our children. Guilt is a major roadblock to building a new life for yourself and to being an effective parent.”
—Stephanie Marston (20th century)