Abstract
The degree representations of the general halting, word, and confluence problems for Markov algorithms are investigated. Each of these problems is shown to represent every r.e. (recursively enumerable) many-one degree but not every r.e. one-one degree of unsolvability. In the course of proving this we also show that every total recursive function is computed by a Markov algorithm which always halts and that the immortality problem for the class of Markov algorithms is Σ o2 -complete.
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This research partially supported by NSF Grant GP 23779.
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Hughes, C.E. Degrees of unsolvability associated with Markov algorithms. International Journal of Computer and Information Sciences 1, 355–365 (1972). https://doi.org/10.1007/BF00987253
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DOI: https://doi.org/10.1007/BF00987253