Abstract
In his celebrated 1936 paper Turing defined a machine to be circular iff it performs an infinite computation outputting only finitely many symbols. We define α as the probability that an arbitrary machine be circular and we prove that α is a random number that goes beyond Ω, the probability that a universal self delimiting machine halts. The algorithmic complexity of α is strictly greater than that of Ω, but similar to the algorithmic complexity of Ω', the halting probability of an oracle machine. What makes α interesting is that it is an example of a highly random number definable without considering oracles.
Honorary co-author.
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Becher, V., Daicz, S., Chaitin, G. (2001). A Highly Random Number. In: Calude, C.S., Dinneen, M.J., Sburlan, S. (eds) Combinatorics, Computability and Logic. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0717-0_6
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DOI: https://doi.org/10.1007/978-1-4471-0717-0_6
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