A function is strongly non-recursive (SNR) if it is eventually different from each recursive function. We obtain hierarchy results for the mass problems associated with computing such functions with varying growth bounds. In particular, there is no least and no greatest Muchnik degree among those of the form SNR consisting of SNR functions bounded by varying recursive bounds f. We show that the connection between SNR functions and canonically immune sets is, in a sense, as strong as that between DNR (diagonally non-recursive) functions and effectively immune sets. Finally, we introduce pandemic numberings, a set-theoretic dual to immunity.
CITATION STYLE
Beros, A. A., Khan, M., Kjos-Hanssen, B., & Nies, A. (2018). From eventually different functions to pandemic numberings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10936 LNCS, pp. 97–106). Springer Verlag. https://doi.org/10.1007/978-3-319-94418-0_10
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