Programmable Logic Has More Computational Power than Fixed Logic

Abstract

In 1964, Elgot and Robinson introduced the Random-Access Stored Program (RASP) machine model ”to capture some of the most salient features of the central processing unit of a modern digital computer.” After four decades of progress in computer science, this model is now somewhat outdated. Intriguingly though, the 1964 paper presented two theorems showing that programs of ’finitely determined’ instructions are properly more powerful if modification of addresses in instructions is permitted during execution than when it is forbidden. In this paper, we celebrate the 40th birthday of these results by using them to prove that allowing programmability of circuits during execution adds extra computational power. To do this, we accord front-line computational status to programmable cir-cuitry, and conduct a theoretical study based on a tradition dating back to Gödel, Turing and Church in the 1930s. In particular, we introduce a new Local Access Stored Circuit (LASC) model of programmable circuitry, intended to form a solid basis for a broad range of future computational research.