Computational complexity of random access stored program machines

Abstract

In this paper we explore the computational complexity measure defined by running times of programs on random access stored program machines, RASP's. The purpose of this work is to study more realistic complexity measures and to provide a setting and some techniques to explore different computer organizations. The more interesting results of this paper are obtained by an argument about the size of the computed functions. For example, we show (without using diagonalization) that there exist arbitrarily complex functions with optimal RASP programs whose running time cannot be improved by any multiplicative constant. We show, furthermore, that these optimal programs cannot be fixed procedures and determine the difference in computation speed between fixed procedures and self-modifying programs. The same technique is used to compare computation speed of machines with and without built-in multiplication. We conclude the paper with a look at machines with associative memory and distributed logic machines.