Complexity of Formal Translations and Speed-Up Results

The purpose of this paper is to give a model for the study of quantitative problems about formal translations from one programming language into another, as well as derive some initial results about the speed of programs produced by translations. The paper also contains a new speed-up result which shows that in any computational complexity measure there exist functions which have arbitrarily large speed-ups but that the size of the speed-up programs must grow non-computably fast.