Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Computing over the reals with addition and order
Selected papers of the workshop on Continuous algorithms and complexity
Computing over the reals with addition and order: higher complexity classes
Journal of Complexity
Complexity and real computation
Complexity and real computation
On the Structure of $\cal NP_\Bbb C$
SIAM Journal on Computing
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
A note on non-complete problems in NP
Journal of Complexity
Classical physics and the Church--Turing Thesis
Journal of the ACM (JACM)
Hypercomputation with quantum adiabatic processes
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Kolmogorov Complexity Theory over the Reals
Electronic Notes in Theoretical Computer Science (ENTCS)
Computational processes, observers and Turing incompleteness
Theoretical Computer Science
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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,+,-,