Unconventional Universal Computation in Babbage's Analytical Engine

Abstract

This paper shows that the programming model of Babbage's Analytical Engine, although unconventional, can be harnessed in order to simulate indirect addressing, a capability that was not included in the original instruction set. That is, in a theoretical sense, the Analytical Engine was as universal as computers we have today. We show how to implement indirect addressing for a working memory of fixed size; this makes it possible to simulate a Turing machine with a finite tape. The result is, of course, only of theoretical and historical interest, without any practical implications.