Further analysis of code generation for a single register machine

Summary

This paper presents a systematic development of the analysis of code generation for the single register machine, from linear to exponential time algorithms. A class of expressions with common subexpressions is introduced which can be optimally coded in quadratic time. A heuristic based on this development is shown to produce code size better than 5/4 that of an optimal coding, for any expression. A method is proposed which would improve this bound, but the most straightforward implementation is shown to require exponential time. Finally, a new analysis of the exponential time bound is presented which more closely describes the complexity of the task of producing optimal code.