An Algebraic Characterization of the Halting Probability
Gregory J. Chaitin · Fundamenta Informaticae · 2007
Using 1947 work of Post showing that the word problem for semigroups is unsolvable, we explicitly exhibit an algebraic characterization of the bits of the halting probability Ω. Our proof closely follows a 1978 formulation of Post's work by M. Davis. The proof is self-contained and not very complicated.