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
On the Power of Real Turing Machines over Binary Inputs
SIAM Journal on Computing
Complexity and real computation
Complexity and real computation
Elimination of constants from machines over algebraically closed fields
Journal of Complexity
A note on non-complete problems in NP
Journal of Complexity
Computable analysis: an introduction
Computable analysis: an introduction
Computable functions and semicomputable sets on many-sorted algebras
Handbook of logic in computer science
Lower Bounds Are Not Easier over the Reals: Inside PH
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
A weak version of the Blum, Shub and Smale model
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Quantum automata and algebraic groups
Journal of Symbolic Computation
An explicit solution to post's problem over the reals
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
(Short) Survey of Real Hypercomputation
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Real computational universality: the word problem for a class of groups with infinite presentation
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
| Hi-index | 0.00 |
Most of the existing work in real number computation theory concentrates on complexity issues rather than computability aspects. Though some natural problems like deciding membership in the Mandelbrot set or in the set of rational numbers are known to be undecidable in the Blum-Shub-Smale (BSS) model of computation over the reals, there has not been much work on different degrees of undecidability. A typical question into this direction is the real version of Post's classical problem: Are there some explicit undecidable problems below the real Halting Problem? In this paper we study three different topics related to such questions: First an extension of a positive answer to Post's problem to the linear setting. We then analyze how additional real constants increase the power of a BSS machine. And finally a real variant of the classical word problem for groups is presented which we establish reducible to and from (that is, complete for) the BSS Halting problem.