An explicit solution to Post's Problem over the reals

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In the BSS model of real number computations we prove a concrete and explicit semi-decidable language to be undecidable yet not reducible from (and thus strictly easier than) the real Halting Language. This solution to Post's Problem over the reals significantly differs from its classical, discrete variant where advanced diagonalization techniques are only known to yield the existence of such intermediate Turing degrees. Then we strengthen the above result and show as well the existence of an uncountable number of incomparable semi-decidable Turing degrees below the real Halting Problem in the BSS model. Again, our proof will give concrete such problems representing these different degrees. Finally we show the corresponding result for the linear BSS model, that is over (R, +, -, <) rather than (R, +, -, x, divided by, <). (c) 2007 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2008-02
Language
English
Article Type
Article; Proceedings Paper
Keywords

COMPLEXITY CLASSES; COMPUTATION; ORDER; SETS

Citation

JOURNAL OF COMPLEXITY, v.24, no.1, pp.3 - 15

ISSN
0885-064X
DOI
10.1016/j.jco.2006.09.004
URI
http://hdl.handle.net/10203/203395
Appears in Collection
CS-Journal Papers(저널논문)
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