Automata and computation

Mark Burgess
 
Faculty of Engineering
Oslo University College

20 October 2000

ENIAC: Electronic Numerical Integrator and Computer v The first ever general-purpose digital electronic computer and the ancestor of most computers in use today. ENIAC was developed by John Mauchly and J. Presper Eckert during World War II at the Moore School of the University of Pennsylvania and was released publicly in 1946.

The machine performed an addition in 200 microseconds, a multiplication in about three milliseconds, and a division in about 30 milliseconds.

In the last two lectures we have looked at how information can be defined, refined, transmitted and modified, sometimes at a cost. We have seen that the evaluation of functions can be viewed as mappings from one set of values to another, and that this can be modelled as the communication or transmission problem. We've also described the transmission problem itself simply as an expression of the causal development of the system:

Source $\rightarrow$ signal $\rightarrow$ Receiver
Cause $\rightarrow$ delay $\rightarrow$ Effect

I now want to pick up on that thread and complete this briefest of introductions to information systems by showing how we apply this idea to build a variety of different kinds of computer. I want to look at this from the viewpoint of a theoretical physicist, rather than as a logician, a computer scientist or an engineer. You can read the other viewpoints in books.

We can play mathematical games with information theory, invent weird representations etc, but if we want to use any of these ideas in practice we have to use a representation grounded in physical law. One could say that the laws of physics become the ultimate low-level protocol for information transfer.