ECCC-Report TR95-025https://eccc.weizmann.ac.il/report/1995/025Comments and Revisions published for TR95-025en-usFri, 11 May 2001 12:36:04 +0300
Comment 1
| Errata in "Analytic Machines" Comment on: TR95-025 |
Günter Hotz,
Thomas Chadzelek
https://eccc.weizmann.ac.il/report/1995/025#comment1We correct some minor errors concerning the definitions of delta-Q-machine and robustness.
Fri, 11 May 2001 12:36:04 +0300https://eccc.weizmann.ac.il/report/1995/025#comment1
Paper TR95-025
| Analytic Machines |
Günter Hotz,
Gero Vierke,
Bjoern Schieffer
https://eccc.weizmann.ac.il/report/1995/025In this paper the $R$-machines defined by Blum, Shub and Smale
are generalized by allowing infinite convergent computations.
The description of real numbers is infinite.
Therefore, considering arithmetic operations on real numbers should
also imply infinite computations on {\em analytic machines}.
We prove that $\R$-computable functions are $\Q$-analytic.
We show that $R$-machines extended by finite sets of
{\em strong analytic} operations are still $\Q$-analytic.
The halting problem of the analytic machines contains the stability
problem of dynamic systems.
It follows with well known methods that this problem is not analytical
decidable.
This is in a sense a stronger result as the {\em numerical undecidable}
stability in the theory of Kolmogoroff, Arnold and Moser.
Wed, 07 Jun 1995 15:11:03 +0300https://eccc.weizmann.ac.il/report/1995/025