Publication Details
Title: A Theory of Computation and Complexity Over the Real Numbers
Author: L. Blum
Group: ICSI Technical Reports
Date: October 1990
PDF: http://www.icsi.berkeley.edu/pubs/techreports/tr-90-058.pdf
Overview:
The classical theory of computation and complexity presupposes all underlying spaces are countable and hence ipso facto cannot handle arbitrary sets of real or complex numbers. Thus e.g., Penrose (1990) acknowledges the difficulty of formulating classically his question: Is the Mandelbrot set recursive? On the other hand, this as well as a number of other inherent questions of decidability and computability over the reals or complex number can be naturally posed and settled within the framework presented in this paper.
Bibliographic Information:
ICSI Technical Report TR-90-058
Bibliographic Reference:
L. Blum. A Theory of Computation and Complexity Over the Real Numbers. ICSI Technical Report TR-90-058, October 1990
Author: L. Blum
Group: ICSI Technical Reports
Date: October 1990
PDF: http://www.icsi.berkeley.edu/pubs/techreports/tr-90-058.pdf
Overview:
The classical theory of computation and complexity presupposes all underlying spaces are countable and hence ipso facto cannot handle arbitrary sets of real or complex numbers. Thus e.g., Penrose (1990) acknowledges the difficulty of formulating classically his question: Is the Mandelbrot set recursive? On the other hand, this as well as a number of other inherent questions of decidability and computability over the reals or complex number can be naturally posed and settled within the framework presented in this paper.
Bibliographic Information:
ICSI Technical Report TR-90-058
Bibliographic Reference:
L. Blum. A Theory of Computation and Complexity Over the Real Numbers. ICSI Technical Report TR-90-058, October 1990