Chaitin's Constant

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.