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Recursively Enumerable Reals and Chaitin Ω Numbers
"... A real is called recursively enumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay [23] and Chaitin [10] we say that an r.e. real dominates an r.e. real if from a good approximation of from below one can compute a good approximation of from b ..."
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A real is called recursively enumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay [23] and Chaitin [10] we say that an r.e. real dominates an r.e. real if from a good approximation of from below one can compute a good approximation of from below. We shall study this relation and characterize it in terms of relations between r.e. sets. Solovay's [23]like numbers are the maximal r.e. real numbers with respect to this order. They are random r.e. real numbers. The halting probability ofa universal selfdelimiting Turing machine (Chaitin's Ω number, [9]) is also a random r.e. real. Solovay showed that any Chaitin Ω number islike. In this paper we show that the converse implication is true as well: any Ωlike real in the unit interval is the halting probability of a universal selfdelimiting Turing machine.
Recursivelyenumerable reals and Chaitin www.elsevier.com/locate/tcs numbers �;��
, 1998
"... Communicated byM. Ito A real is called recursivelyenumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay(unpublished manuscript, IBM Thomas J. Watson ..."
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Communicated byM. Ito A real is called recursivelyenumerable if it is the limit of a recursive, increasing, converging sequence of rationals. Following Solovay(unpublished manuscript, IBM Thomas J. Watson