An Algebraic Characterization of the Halting Probability

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 selfcontained and not very complicated.

• Type: Journal
• Year: 2007
• Where: FUIN
• Authors: Gregory J. Chaitin
• Keywords: Algebraic Characterization, FUIN 2007, Halting Probability, Word Problem