Some recent developments on Shannon's General Purpose Analog Computer
✍ Scribed by Daniel Silva Graça
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 218 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
This paper revisits one of the first models of analog computation, the General Purpose Analog Computer (GPAC). In particular, we restrict our attention to the improved model presented in [11] and we show that it can be further refined. With this we prove the following: (i) the previous model can be simplified; (ii) it admits extensions having close connections with the class of smooth continuous time dynamical systems. As a consequence, we conclude that some of these extensions achieve Turing universality. Finally, it is shown that if we introduce a new notion of computability for the GPAC, based on ideas from computable analysis, then one can compute transcendentally transcendental functions such as the Gamma function or Riemann's Zeta function. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)