Formally Unsolvable Problems in Software Engineering

Engineering has been defined as the solution of practical problems using mathematical and scientific principles. Is it possible to apply mathematical and scientific principles to the solution of important problems in software engineering, such as the prediction of development schedules and the assessment of productivity and quality? The debate over this question is familiar. In this article, we will look at software engineering from a different point of view, that of algorithmic complexity. Algorithmic complexity (see sidebar) defines the complexity of a digital object to be the length of the shortest computer program that produces that object. We will find that algorithmic complexity results can be directly interpreted as indicating that software development schedules, productivity, and reliability cannot be objectively and feasibly estimated and so will remain a matter of intuition.