## Some recent developments on Shannon’s general purpose analog computer

### Cached

### Download Links

Venue: | Mathematical Logic Quarterly |

Citations: | 18 - 7 self |

### BibTeX

@ARTICLE{Graça_somerecent,

author = {Daniel Silva Graça},

title = {Some recent developments on Shannon’s general purpose analog computer},

journal = {Mathematical Logic Quarterly},

year = {},

pages = {473--485}

}

### OpenURL

### 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. 1