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An Algebraic Characterization of the Halting Probability

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 self-contained and not very complicated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Fundamenta Informaticae IOS Press

An Algebraic Characterization of the Halting Probability

Chaitin, Gregory
Fundamenta Informaticae , Volume 79 (1) – Jan 1, 2007
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Publisher
IOS Press
Copyright
Copyright © 2007 by IOS Press, Inc
ISSN
0169-2968
eISSN
1875-8681
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Abstract

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.

Journal

Fundamenta Informaticae – IOS Press

Published: Jan 1, 2007

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