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 ( as the probability that an arbitrary machine be circular and we prove that is a random number that goes beyond $2, the probability that a universal self alelimiting machine halts. The algorithmic complexity of c is strictly greater than that of $2, but similar to the algorithmic complexity of 2 , the halting probability of an oracle machine. What makes ( interesting is that it is an example of a highly random number definable without considering oracles.

Citations