Wesley Calvert (Murray State University) |
Ken Kramer (Queens College & CUNY Graduate Center) |
Russell Miller (Queens College & CUNY Graduate Center) |
We examine the relation of BSS-reducibility on subsets of the real numbers. The question was asked recently (and anonymously) whether it is possible for the halting problem H in BSS-computation to be BSS-reducible to a countable set. Intuitively, it seems that a countable set ought not to contain enough information to decide membership in a reasonably complex (uncountable) set such as H. We confirm this intuition, and prove a more general theorem linking the cardinality of the oracle set to the cardinality, in a local sense, of the set which it computes. We also mention other recent results on BSS-computation and algebraic real numbers. |
ArXived at: https://dx.doi.org/10.4204/EPTCS.24.10 | bibtex | |
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