David Cash, Dennis Hofheinz, et al.
Journal of Cryptology
We present a model for computation over the reals or an arbitrary (ordered) ring R. In this general setting, we obtain universal machines, partial recursive functions, as well as NP-complete problems. While our theory reflects the classical over Z (e.g., the computable functions are the recursive functions) it also reflects the special mathematical character of the underlying ring R (e.g., complements of Julia sets provide natural examples of R. E. undecidable sets over the reals) and provides a natural setting for studying foundational issues concerning algorithms in numerical analysis. © 1989 American Mathematical Society.
David Cash, Dennis Hofheinz, et al.
Journal of Cryptology
Ehud Altman, Kenneth R. Brown, et al.
PRX Quantum
Guo-Jun Qi, Charu Aggarwal, et al.
IEEE TPAMI
J. LaRue, C. Ting
Proceedings of SPIE 1989