Separation of complexity classes in Koiran's weak model
Selected papers of the workshop on Continuous algorithms and complexity
P ≠ NP over the nonstandard reals implies P ≠ NP over R
Selected papers of the workshop on Continuous algorithms and 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
On the Structure of Valiant's Complexity Classes
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Exotic Quantifiers, Complexity Classes, and Complete Problems
Foundations of Computational Mathematics
On Ladner's Result for a Class of Real Machines with Restricted Use of Constants
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
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We study the question whether there are analogues of Ladner@?s result in the computational model of Blum, Shub and Smale. It is known that in the complex and the additive BSS model a pure analogue holds, i.e. there are non-complete problems in NP@?P assuming NPP. In the (full) real number model only a non-uniform version is known. We define a new variant which seems relatively close to the full real number model. In this variant inputs can be treated as in the full model whereas real machine constants can be used in a restricted way only. Our main result shows that in this restricted model Ladner@?s result holds. Our techniques analyze a class P/const that has been known previously to be crucial for this kind of results. By topological arguments relying on the polyhedral structure of certain sets of machine constants we show that this class coincides with the new restricted version of P"R, thus implying Ladner@?s result.